problem vs case

problem and case both are nouns.

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

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

problem (noun)	case (noun)
a source of difficulty	a comprehensive term for any proceeding in a court of law whereby an individual seeks a legal remedy
a question raised for consideration or solution	a portable container for carrying several objects
a state of difficulty that needs to be resolved	a glass container used to store and display items in a shop or museum or home
	bed linen consisting of a cover for a pillow
	(printing) the receptacle in which a compositor has his type, which is divided into compartments for the different letters, spaces, or numbers
	the housing or outer covering of something
	the enclosing frame around a door or window opening
	an enveloping structure or covering enclosing an animal or plant organ or part
	the actual state of things
	nouns or pronouns or adjectives (often marked by inflection) related in some way to other words in a sentence
	a statement of facts and reasons used to support an argument
	a problem requiring investigation
	a specific size and style of type within a type family
	an occurrence of something
	a person who is subjected to experimental or other observational procedures; someone who is an object of investigation
	a person requiring professional services
	a person of a specified kind (usually with many eccentricities)
	the quantity contained in a case
	a special set of circumstances
	a specific state of mind that is temporary

problem (verb)	case (verb)
	enclose in, or as if in, a case
	look over, usually with the intention to rob