Emotional maturity and maturity differ slightly:

Emotional maturity is defined as how well you are able to respond to situations, control your emotions and behave in an adult manner when dealing with others.

Definition of mature: fully developed in body or mind, as a person: She was a mature woman who took her family responsibilities seriously.

In psychology, maturity is the ability to respond to the environment in an appropriate manner.

They seem to be close in definition but emotional maturity deals more so with emotions and our reactions to emotionally charged situations.