The move from Twitter to X changed the brand but not the plumbing. Both twitter.com and x.com resolve to identical posts, old links were never broken, and t.co short links from the share sheet expand to either domain. If you have a bookmarked twitter.com URL from years ago it will still work here. There is no need to convert anything by hand.
Video quality depends more on the poster than on the platform. X accepts up to 1080p from standard accounts, and Premium subscribers can upload longer clips at higher quality. What this means practically is that two posts can look identical in the timeline while storing very different files underneath — one at 1080p and one at 480p, because that is what each poster uploaded. We list what genuinely exists for the post you pasted rather than promising a resolution that may not be there.
The GIF behaviour is the thing most worth understanding. When anyone attaches a GIF to a post, X immediately converts it to a silent MP4 and plays it on a loop with a small GIF badge in the corner. From that point on there is no GIF anywhere in the system. Saving it gives you a video file, which surprises people who expected an animated image they could drop into a chat.
That is a genuine format problem rather than a downloading one, so the fix is a real conversion: taking the MP4 X stores and rebuilding an animated GIF from it. That conversion loses colour depth, because GIF supports only 256 colours per frame, and it usually produces a much larger file than the MP4 it came from. Both trade-offs are unavoidable, which is why we offer the MP4 as well and let you pick.