Do atheists simply not believe in God or believe in no God?

It's a subtle difference as the former would result in apathy (after all, I don't believe in unicorns, but I'm not on a crusade against unicorns) and the latter would result in active proselytizing for atheist converts. So is atheism an active belief system akin to a religion? If not, then why are atheists not merely apathetic? Why is it they proselytize their "faith" so actively (in a similar way to militant Islamic extremists)?