Briefly: manhwa is the Korean reading of the word 漫画, while manga is the Japanese reading.1 In their respective languages, both words basically mean the same thing - "comics". In English, we use the Korean reading manhwa to refer to Korean comics, and the Japanese reading manga to refer to Japanese comics.
Why do we have different words for these things? Because manhwa and manga are not the same thing.
To explain what I mean, let me backtrack a bit and talk about why we don't just call manga "comics". I know that these days there's something of a backlash against the idea that "manga" is a distinct thing from "comics", presumably a reaction against '90s-era weeabooism and orientalism that identifies Japanese art as some sort of elevated form that is beyond comparison with the art of the West.
There is a kernel of truth in this backlash, but it's been taken too far. Reasonable people today will probably agree that there isn't anything about manga that makes them inherently superior to Western comics - but it is certainly the case that manga and Western comics are different. In fact, aside from being of the same medium, manga and Western comics (for the most part) have essentially nothing in common! Art styles, typical plots / subject matter, character archetypes, form factors, publication methodologies, etc. all differ between manga and Western comics.
Now, manhwa and manga are more closely related than manga and Western comics, but the same principle still applies - there are salient differences between the two forms, which is why we often talk about them using two different words. Foremost among the differences is the fact that they're largely written by two different groups of people, and thus tend to reflect the interests of two different cultures. (Try telling a Korean person that their culture is basically Japanese, or vice versa - they probably won't be happy!)
In closing, I will reply to this claim of yours:
In the end they are both comics with usually (bit Dependant on the artist/writer off course) same art/story building and the likes.
There's more to art than just medium. Medium matters, but so does content, and it would be a gross oversimplification to claim that content of manga and manhwa are essentially the same.
1 More or less, anyway, modulo issues of character simplification.