Suppose a person is found dead, and it's investigated as a possible murder.
How would such a case be characterized in criminal law - a murder hypothesis, murder theory, murder mystery?
EDIT: As noted in the comments below, it would be helpful to know what such a case would be called even after it was officially closed (after not being solved for a long period of time, for example).
To cover my bases, I should also add a second possibility: It is known for a fact that a person was murdered. The only question is WHO DID IT? (If that makes things too complicated, I can delete this and revert to my original question.)
Would the same terminology be applied to each case?