To "earn a living" means to make enough money to pay for your food, rent, car, and so on. You tell what job you're talking about with the phrase "earn a living as ___".

Do you think it's realistic to hope to earn a living as a musician?

The phrase "earn a good living" means to make more than just the basic amount necessary. A person who "earns a good living" isn't rich, but isn't poor either.

It used to be that you could earn a good living as a driver, but these days it's hard.