Whether or not you make money from it is immaterial to the question - what you are is not necessarily defined by what you do to pay the rent. A musician is someone who makes music. That to me includes singing, though I know many disagree. The Copper family may not have considered themselves "musicians" but try telling them that they're not "singers" just because they don't make their living from it. The initial question said "musician", not "professional musician" or even "good musician" - they're not all the same thing. How can you play music without being a musician? Perhaps the question should be "when do you start admitting to others that you're a musician?"

Andrew