Nope. Mush is just more informal than mate. So, for example. If I see a normal friend in the street I'd shout 'Hello mate, how ya doing?'. But if I saw a best friend or someone I'd known for years I might shout out 'Whats happening mush?' and just to make it more confusing when you're in South Wales they say 'Sappening mush?' Which is just a quicker way of saying 'Whats happening'.