growing pains vs problem

growing pains and problem both are nouns.

Word	Noun	Adjective	Verb	Adverb
growing pains	Yes	No	No	No
problem	Yes	No	No	No

As nouns, problem is a hypernym of growing pains; that is, problem is a word with a broader meaning than growing pains:

growing pains: problems that arise in enlarging an enterprise (especially in the early stages)
problem: a source of difficulty

Other hypernyms of growing pains include trouble.

growing pains (noun)	problem (noun)
problems that arise in enlarging an enterprise (especially in the early stages)	a source of difficulty
emotional distress arising during adolescence	a question raised for consideration or solution
pain in muscles or joints sometimes experienced by children and often attributed to rapid growth	a state of difficulty that needs to be resolved