There is a subtle difference in how they are most often used: "your grade depends on your test scores" = Your test scores determine what your grade will be. "Whether we go to Paris is contingent on whether I can get time off work" = The trip will not happen unless I get time off. They can both be used in both ways, but "contingent on" is most often used to imply that something will or will not happen. Also, as Marlana said, "depends on" is used more often in informal speech. PS: A "contingency" is something that might or might not happen. "The boat probably will not sink, but we must prepare for all contingencies. Therefore, everyone must wear a life vest."

There aren't any differences in meaning. The two words mean the same thing, but what makes them different is how you may want to sound to your audience. What are you using the word for exactly? Are you writing a thesis, or just having a conversation with people? In English we use "dependent" all the time. We use "contingent" very seldom in regular conversations. I do have an opinion on words like this: To me, words like contingent are used in situations when you hear a press conference, you're attending a lecture, or when you read reference materials. Sometimes when one word is already used, people will use synonyms in order to reiterate a point soon after so they don't sound repetitive. (I'm a writer; I do this all the time.) Sometimes, people increase their vocabulary and use "big words" (as we joke about in English). If you say "contingent" to someone and you didn't know the meaning until now, likely someone else didn't know the meaning either. People who use language like this during friendly conversations tend to appear educated as they have broadened their vocabulary with words that are correct (but not used as often as the average speaker). But if it becomes a habit, it can seem high-handed.

Both words are closely linked and may be used interchangeably In situations that are conditioned or determined by another situation , For example 1-One could say “ our trip to the beach is dependent on the weather.” 2- Our plans for today are contingent on the weather

Thank you very much, Laura.

Edited, answered.