It appears as if only "season 1" is actually called "Sailor Moon". The rest are called different things:
Sailor Moon (1992–93).
Sailor Moon R (1993–94).
Sailor Moon S (1994–95).
Sailor Moon SuperS (1995–96).
Sailor Moon Sailor Stars (1996–97).
You are correct. Only Season 1 is actually called Bishoujo Senshi Seeraamuun (Beautiful Solider Sailormoon = 『美少女戦士セーラームーン』) and is often referred to as Sailormoon (Seeraamuun =『セーラームーン』) (written run together on official merchandise) or, lesson commonly, referred to as SeraMun (『セラムン』) for short.
(In other countries, the title is generally called Sailor Moon, splitting the name into 2 English words. Because this StackExchange is mostly read by people outside of Japan, I will use "Sailor Moon" to refer to the original show in this post.)
The second season uses that same Bishoujo Senshi Seeraa Muun to indicate that it is a continuation of the same show, but adds the letter R, pronounced as "Aaru" (R = 「アール」). The company had various words starting with R in mind, but the meaning of the R is left ambiguous and up to the viewers' imaginations. The addition of something tacked on after the prior season's title signals that this is a different season and story arc but a continuation of the same show.
The third season uses that same Bishoujo Senshi Seeraa Muun and adds what looks like the letter S but is not pronounced as "S"; it is instead pronounced as "Suupaa" (Super = 「スーパー」).
The fourth season uses that same Bishoujo Senshi Seeraa Muun but instead of an S pronounced as "Suupaa," it changes to "Suupaazu" (SuperS = 「スーパーズ」), which is not pronounced as "Super S" but, rather, is pronounced as "Supers" as if the word "super" could become a plural.
The fourth season uses that same Bishoujo Senshi Seeraa Muun and adds "Seeraasutaazu" (Sailorstars = 「セーラースターズ」), where, in official merchandise, Sailorstars is a single run-together word (whereas overseas, it is usually broken apart into 2 English words: "Sailor Stars").
Three of the seasons each featured a theatrical film, one season also included an anime adaption of Ami-chan no Hatsukoi (Ami-chan's First Love = 『亜美ちゃんの初恋』) side-story manga as an anime short, and there were also specials. Each film and special used the title of the current season at the time that they were released.
The seasons are liberally-adapted from the story arcs used in the manga:
Season 1 corresponds to the Dark Kingdom arc,
R (Season 2) corresponds to the Black Moon arc (with the original addition of the Makaiju [Tree of the Demon World = 魔界樹]) arc,
S (Season 3) corresponds to the Mugen (Infinity = 「無限」) arc,
SuperS (Season 4) corresponds to the Yume (Dream = 「夢」) arc,
Sailorstars (Season 5) corresponds to the Stars arc (with the addition of a brief 6-episode arc featuring the return of the villain from Season 4 before it starts the Stars arc proper).
Interestingly, only the title of the 5th manga arc was included in the title of the 5th anime season.
Is this common in Japan?
. . .
Up until today, I thought that these were some sort of separate "alternative shows".
Yes, this is very common in Japan: the same basic title alerts the potential viewer that this is the show you already know of (so people who enjoyed the prior season but aren't hardcore enough to be following when the next one will begin airing can notice the title they're familiar with when they look at TV listings), but tacking on the addition of something (whether a letter, word, multiple words, and/or typographical symbol) communicates that this is a new story arc (so if you didn't watch the previous arc[s], it's not a bad place to jump in for the first time, or to jump back in). So if you never watched the first season, you could realize from this title style that you can start watching from the start of the new arc without feeling completely lost as to what is going on in the plot, but you would be aware that the characters' relationships are already established and ongoing from a prior arc.
This was originally the case with the franchise Purekyua (Precure = 『プレキュア』) (which is called "Pretty Cure" outside of Japan). It started like Sailor Moon did, with Futari ha Purekyua (The Two of Us are Precures『ふたりはプリキュア』), got a second season called Futari ha Purekyua Max Heart (『ふたりはプリキュア Max Heart』, and a third season called Futari ha Purekyua Splash Star (『ふたりはプリキュア Splash Star』): in each case, the base title was the same but something was tacked on to the end to indicate a new story arc featuring the same ongoing characters.
What is less common in Japan but has risen in number after the era of Sailor Moon is a (perhaps confusingly) similar format for alternate shows derived from a common premise. After its initial three seasons of Futari ha Purekyua, the Precure franchise shifted to a system different from that of Sailor Moon. This franchise morphed into many series which each have their own protagonists, villains, worlds, and plots; the only thing that ties all of them together is that the protagonists are always a type of mahou shoujo (magical girl) called precures (regardless of how different from each other their visuals and abilities and backstory were in each series), and the animation company began making crossover theatrical films/specials where characters from different worlds meet each other and, in recent years, they even make a few crossover TV show episodes - but every series is separate and self-contained, and does not require having watched any of the other series.
The titles of each of these series always include the word "precure," but other than that, the titles differ (for example, Furesshu Purikyua! (Fresh Precure! =『フレッシュプリキュア!』), Sumairu Purikyua! (Smile Precure! = 『スマイルプリキュア!』), Dokidoki! Purecure (Heart-pounding! Precure = 『ドキドキ!プリキュア』), HUGtto! Precure (HUG-squeeze! Precure『HUGっと!プリキュア』), and Sutaa☆Toinkuru Purekyua (Star☆Twinkle Precure =『スター☆トゥインクルプリキュア』).
In a rare case, the creators decided to add a subsequent season to a highly-popular particular set of characters, in which case they used the title style of Sailor Moon and Futari ha Purekyua, by tacking something onto the end of the previous season's title: Yes! Precure5 (Iesu! Purekyua5 =『Yes！プリキュア5 』) got a second season called Yes! Precure5GoGo! (Yes! Purekyua5GoGo! =『Yes！プリキュア5GoGo！』).
Do they not like to call things "seasons" (USA) or "series" (UK)?
This is a confusing point: the Japanese use both words somewhat interchangeably (Season 1 can be referred to as dai1shiizuun (1st season =「第１シーズン」) or as dai1shiriizu = (first series = 「第１シリーズ」), but they also use the word shiriizu (series =「シリーズ」) to refer to an entire franchise like Precure even though it is comprised of disparate shows.
There was also:
Pretty Guardian Sailor Moon (2003).
Sailor Moon Crystal (2014).
But those seem like much later and quite different.
"Pretty Guardian Sailor Moon" is what fans outside of Japan took to calling the live-action TV series in order to easily differentiate it amongst themselves from the prior anime, but its Japanese title was exactly the same as that of the 5-season-long anime: Bishoujo Senshi Seeraamuun (Beautiful Solider Sailormoon = 『美少女戦士セーラームーン』), so Japanese fans in Japan do not consider the live-action series to have a different title from the manga or from the prior anime in any sense.
Rather than think of this live-action series as a reboot of the anime, it is more accurate to think of it as a different adaption from the original manga. It does not expect any former knowledge of the characters or plots from either the manga or the prior anime, and starts from the beginning of the first manga arc. Like the previous anime series had done, it took some liberties by featuring original content not found in either of the prior versions, such as its Dark Mercury, Sailor Luna, and puppeteered Princess Sailor Moon personas.
The Bishoujo Senshi Seeraamuun Crystal (Beautiful Solider Sailormoon Crystal = 『美少女戦士セーラームーン Crystal』) web anime series and its Gekijouban Bishoujo Senshi Seeraamuun Eternal (Theatrical Edition: Beautiful Solider Sailormoon Eternal = 『劇場版 美少女戦士セーラームーン Eternal』) theatrical movies are a much later adaption from the original manga. It is the first Sailor Moon series that had an international fandom in mind in addition to the Japanese fandom, so it was released as Pretty Guardian Sailor Moon Crystal as its simultaneous official English title (despite the fact that senshi - which means 'soldier,' 'combatant,' or 'warrior' and is made up of the Chinese characters for 'war' + 'samurai' or 'warrior' - does not accurately translate to the less-violent/aggressive image of the English word 'guardian'; it uses this to match the official English retroactively-applied to the manga that the mangaka [manga artist], Takeuchi Naoko, preferred).
At first, Crystal aimed to mimic the manga as closely as possible, avoiding any deviations from the manga that had appeared in the prior beloved anime. However, after Crystal severely bombed with Japanese audiences (likely due to its poor characterization, plot, and animation quality in comparison to the character development/plot/art quality of the prior long-running series), the director and character designer were both scrapped and elements from the prior anime were then abruptly re-incorporated, but this did not salvage Crystal amongst Japanese viewers, most of whom had written it off after the first episode. It did so poorly that instead of being able to finance an entire Season 4 as previously intended, the Dream arc was compressed down into a 2-part theatrical movie. The Eternal films also bombed at the Japanese box office, not even making it into the Top 10 Anime Films in movie theaters during the Part 1 release in January 2021 (notice that is not a list of the Top 10 films released in January 2021, or even the Top 10 anime films released in January, but was the box office ranking for all anime films in theaters at that time, which included some that had even already been in theaters for weeks or even months before Eternal Part 1 came out, and it couldn't even attract attention/interest away from those). (At the time of writing this post, whether or not an attempt to adapt the Stars arc into any sort of Crystal format after such financial failures is unknown. If it does happen, it would likely be due to hopes for overseas interest, rather than for domestic Japanese interest in such a project.)
Note: I haven't yet quite finished the first season, so I don't know how the rest is, but I have a strong feeling that it will lose its charm once Usagi and the other girls know that she is a Moon princess and all that stuff. I like the first few episodes the best, which I watched when I was still a kid, because everything about the demons and even Luna is not yet explained and Usagi was just a confused and clumsy school girl who regularly transforms into Sailor Moon.
If you do not feel that you want to watch through an entire 200 episodes, I would strongly suggest skipping ahead to episode 173 after you finish the first arc to resume from the 7th episode of the Sailorstars season, which is when the Stars arc begins.
As a child, I enjoyed Sailorstars most of all the seasons because it was fun and charming but, as an adult (although I have enjoyed noticing commentary about Japanese society in the first season that had gone over my head as a child), I most enjoy re-watching Sailorstars because it has very deep, poignant, and enduringly useful themes, such as intercultural understanding, gender, punishment vs. forgiveness, etc. It is also impressive when you contrast the maturity of characters in the 5th season with how they were in the 1st season.
Furthermore, some characters appear for the first time in the 5th season: one of them, Seiya Kou (a.k.a. Sailor Star Fighter), even placed in the Top 10 Sailor Moon characters of all time in NHK's Zen Bishoujo Senshi Seeraamuun Anime Dai Touhyou (All "Beautiful Solider Sailormoon" Anime Grand Election = 『全美少女戦士セーラームーンアニメ大投票』) in 2021. Despite many viewers never having watched that far into the series, the love for this character is so strong among the fans who have watched through to the end that, 25 years later, he is fondly remembered enough to beat out many characters who are much more generally well-known.