problem vs toughie

problem and toughie both are nouns.

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

As nouns, toughie is a hyponym of problem; that is, toughie is a word with a more specific, narrower meaning than problem:

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