What's the difference between an emoji version and a Unicode version?

Unicode and Emoji versions aren't the same. Unicode is the full text standard (Unicode 15.0, 16.0, etc.), while Emoji is a focused sub-standard that tracks only emoji additions (Emoji 15.0, 15.1, 16.0).

Since 2019 they have been aligned — Emoji 15.0 was released alongside Unicode 15.0. But before that, they drifted independently (Emoji 4.0 was part of Unicode 9.0, for instance).