I’m in the brass band or I’m in the brass band club?

Stupid question about bukatsu in Japan. I really need an answer. There are many Japanese students and even teachers who say " I'm in the brass band club" but isn't it redundant? Isn't it better or correct to just say I'm in the brass band ? I'm in the band?
Band is a group of musicians and club is a group of people with a common purpose/interest. Which one do you prefer? Should I correct my students ?

by bananasuki2022