case vs problem

case and problem both are nouns.

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

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

case (noun)	problem (noun)
a comprehensive term for any proceeding in a court of law whereby an individual seeks a legal remedy	a source of difficulty
a portable container for carrying several objects	a question raised for consideration or solution
a glass container used to store and display items in a shop or museum or home	a state of difficulty that needs to be resolved
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

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