Funny is a very general term, which could include being facetious. It generally means 'humorous' but can also mean 'strange'.
Facetious is pretty specific. It's kind of like being sarcastic, but without being very negative.
Imagine someone recently got out of prison and then got married.
You say to your friend who tells you about it, "Wow, this time he got a life sentence." Your friend says, "That's not a very nice thing to say,"
You say, "I was just being facetious."