A case can be a container/box with a set of identical items. (E.g. case of beer cans) Casing is the actual packaging. The can holding the beer, the plastic/box binding the cans together, eggshell, plastic protectors on new gadgets etc. The word case has other various meanings though, it can be a particular situation or an example of something happening. I hope that's helpful:)

Generally, you can put something in and out of a case, while casing is attached to the object. So a phone comes from the factory 'encased' in casing (the outside layer), and the extra thing you buy to protect it is a case.