Dyrone said:
But there is actually a word for this: cinemagraph. It means "still photographs in which a minor and repeated movement occurs". It doesn't seem like it's used as a tag around here, but maybe we could start using it.

Hmm, i never knew there was a word for it, thanks for answering!

Also i never realized that my post was already asked for, oops.

AbiCordo said:
Tag for when - while the image is animated - it has either very minimal animation, or even animation that is barely noticeable?

I think a tag for that kind of thing might actually be pretty useful, as people are likely to complain when an "animated" image seems like it's almost a normal JPG/non-animated PNG.