So I've never played League, but after getting hooked on Arcane I discovered a Youtuber named TBskyen who among other things reviews League character designs as well as their skins.
My understanding from his videos is that the skins will often completely re-imagine the character with a different theme, with the higher priced ones even coming with completely new animations. For example the Star Guardian skin line turns characters such as Lux and Jinx into magical girls.
In this case: Vi and Caitlyn look different because this is from a skin line that re-imagines them as high schoolers.