Yes they both have a similar meaning. They are ADJECTIVES, not nouns. It's mandatory to wear school uniform, it's also compulsory. Both also have Latin roots. They are linked to the words mandate and compel or compulse. Language is often a matter of preference, so use whichever you prefer, but use them both...That's my advice, also see here: https://ell.stackexchange.com/questions/3715/differences-between-mandatory-and-compulsory#:~:text=Strictly%20speaking%2C%20there%20is%20some,difference%20between%20the%20two%20words.