The story jumps forward two years with the start of Maximum, and takes on a slightly more serious tone, perhaps due to the switch from a shōnen to a seinen magazine.
The publishers were sympathetic, and the manga resumed in 1998 as Trigun Maximum (トライガンマキシマム Toraigan Makishimamu?).
[The anime series] was broadcast on TV Tokyo from April 1 to September 30, 1998 . . .
So, Trigun Maximum was a continuation of Trigun. Trigun was ended before it was intended because the magazine where it was published, Shōnen Captain, was cancelled. The anime is based on Trigun only, as its air date was the same year that Trigun Maximum started publication. You'll notice the anime diverges from the manga quite a bit though.
If people say one or the other is a "reimagining," this is most likely due to the choice of the people making the anime to change the story in order to give it an actual ending. I would not really call this a "reimagining," though: it is more like they came up with an alternate canon because the manga was not finished. In other words, the anime started out based on the manga, but then it came up with its own story independently, and the manga author did what he planned to do from the beginning, without being influenced by the anime. It's possible that people making the anime may have asked the manga author for input on events that he had planned that he had not yet written, but I do not know this for a fact.