You can look a little closer at each word's history (etymology) and the differences become clear. "Ridiculous" is connected to the Latin word "ridere" (to laugh), so this word literally means "laughable". It has a comic sense. "Stupid" refers to shock and an inability to communicate properly. Look at the modern English word "stupor" and you'll see the connection. It implies a uselessness, which may or may not be funny.

Well, these words are synonyms, but stupid is more suitable to describe a person or an animal and ridiculous is more often used to describe situations, however, you can tell that a person is ridiculous as well so... there is no real difference between these to, there might be a slight difference of usage in the earlier times but that's just it.