I think in the case of an adult, 'Emotional Retardation' is a more apt term to be replaced or used exchangeably with 'Emotional Immaturity.'
A person's psychological development has only two paths to follow; you either grow or you regress. If a person grows up to the age of adulthood without ever feeding their mind with material that foster their emotional development either by influence, observation or deliberate learning, I think their emotional cognition gets somewhat rotten rather than remaining stagnant. Because by behavioural action if you analyse the emotional thought process of let's a 3 or 4 years old emotionally developing/undeveloped child (who can be said to be immature) and an 'emotionally immature' 45 years old adult, in comparison, you find that they are different. The child is somewhat emotionally not correct but straight and flexible. On the other hand the adult has a rough and stone cold, repelling resistance (or messed up) emotional thinking. Like a complex machine having a problem that is beyond fixing.. I don't think 'immaturity' does justice in describing the adult.
I am not a native English speaker. So it's a little bit hard to express myself better on this
I am hoping to know more about the emotional psychology of it all. Thanks..