There are countless animation styles, as many as there are 3D artists in the world. Since art is ultimately interpretation, each studio and each animator can set a set of rules and choose the most appropriate techniques to define a type of animation.
This decision may originate from artistic or budgetary reasons. However, broadly speaking, there are 3 main types of 3D Animation: Realistic, Cartoon and Snappy and the most common is to find hybrids that define the personality or style of each video game.