As best I can tell, Trigun: Stampede is a reimagining and seems to be in prequel territory at this point, but with elements of the original included in this earlier time frame.
You can tell that in the context of the original series, this definitely takes place before. In fact it basically leads up to the precursor event that is constantly referenced in the beginning of the original (The July Incident) as to why Vash has that insane bounty on his head. However, there are multiple events from the original that are retold here as if they are in the present; there are tons of characters that Vash supposedly meets for the first time in the original that he mixes it up with in Stampede, so he should have clearly known these people in the original if it was a true prequel.
That said, while I absolutely love the original, this easily feels like the superior version thus far. Everything flows better and because of the "prequel" ground they tread, you end up with a much better understanding of what is actually going on with the overall story. Vash/Knives are much better explained, as are the "Plants" and where they come from and what they actually are. The actual origins of the humans on the planet and project SEEDS are fleshed out. And there are other factions (2 more besides humans and Knives/the Plants), for lack of a better term, that are revealed and seem to have a major role to play in the future. The final scene and post credit reveal set up the 4th side in the story as being a major factor in the next season. The ending also sets up the reveal in season 2 of that character everyone noticed was conspicuously absent from this version for no apparent reason.
All in all, I absolutely love this show. Can not wait for season 2 to see where they take it next. Will it follow more of the events of the original now that the timelines are in the same place? How will that mix with other sides at play now, especially the one from the post credit scene? Will they tread completely new ground that makes the next season seem more like a sequel to the original instead? I've no idea, but I'm hyped.
tl;dr They Final Fantasy 7 Remaked Trigun and they did a really good job.