A case as you have put it above could mean packaging. A display case is a stand/cupboard in which you display products.

A computer has a case; it's the plastic shell in which the computer is housed. "Brand X computers have boring, beige, squared-off cases. Brand Y computers have stylish, colorful cases with dramatic industrial design." "Display" means how the product is shown to customers in a store. "In store X, the computers are displayed locked inside glass display cases, and turned off. You can't touch them or see them working. In store Y, the computers are displayed on a table, turned on, and working. You can see them, touch them, and try them out."

A case is a hardened (often box like) cover . A display case is a special cover with transparent elements. Its purpose to show what is inside.