difference between conventional morality and moral maturity?

Answer 1

Conventional morality could be defined as doing something or believing something is right because that's what society teaches should be done or is right.

Moral maturity is doing what is right because you believe rationally, experientially, spiritually, or otherwise that it is the right thing to do. The key is that it is the result of an independent process.

Now the two are not mutually exclusive. Just because one's sense of morality comes to them through others, does not mean it is arbitrary. Children learn conventional morality first, and in an ideal world it is taught to them by people who have come to understand what is right through independent reflection -- people who are morally mature.

Moral maturity most often comes by understanding the principles upon which the conventional morality that they learned as children are based, and then choosing to accept or reject it based upon personal consideration.

Clear as mud?

Answer 2

Like the difference between training wheels and "knowing" how to keep your balance on the bike without them -- when you know how it feels to live right (having learned a lot of it the hard way), you don't have to look up the rules in someone's book.