toughie vs problem

toughie and problem both are nouns.

Word	Noun	Adjective	Verb	Adverb
toughie	Yes	No	No	No
problem	Yes	No	No	No

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

toughie (noun)	problem (noun)
a particularly difficult or baffling question or problem	a source of difficulty
an aggressive and violent young criminal	a question raised for consideration or solution
	a state of difficulty that needs to be resolved