We all know that all 4 categories differ. But what is the difference?
The simple way to explain this (there is lots of other definitions) is that Comic and Cartoon in the Western World is the same as Manga an Anime in Japan. Comic and Manga refer to the medium of illustrated stories on physical pages, whereas Cartoon and Anime refer to illustrated stories on TV (Source).
Whilst both are caricatures and drawn by artists they are different in a number of aspects. The general rule of thumb is that Anime is closer to reality, as the characters have more distinct features and movement. Cartoon on the other hand is often two-dimensional and is typically non-realistic and simplifying intended for satire (Source).