Animate is a vector based animation program that has a full suite of drawing tools. Animate can publish to a wide array of platforms and uses ActionScript as a progamming language.
After Effects is like Photoshop for video. It does not have very many drawing tools. Footage is typically imported into AE and edited using AE's very powerful suite of tools and endless supply of native and 3rd party plugins. You can use scripts to control/create cool effects.
There are MANY difference beyond that and it would take hours to list them all here. Best to look at both product pages on Adobe website to compare features.