A briefcase is a rectangular bag that is most often used by professional workers. Briefcases are usually black and made of leather.
A case is something that goes around something else, for storage and protection. Expensive things that need to be kept safe are usually kept in cases. The picture is of a violin and its case, but it is common to see guitar cases and glasses cases too.
Case might also be a word for a situation or the state of things, as in "take some money in case you need it".