Yes, I agree that 'take part in' and 'participate in' are the same and that 'join' is different. If a person said, "I joined a club," I might think that they go there regularly and that they are a member. However, if they were to say, "I participated in club activities" or "I took part in club activities," I would not be able to tell if they were a member of the club or if they were just visiting the club one time.

I think "take part in" and "participate in" are the same but "join" is a little different. Before you "take part in" or "participate in" an activity, you must first "join". For example: I joined the school football team but I didn't take part in the game. I joined the theatre and took part in a production. Also, "join" can mean to put two things together.

They are the same.