Inside the heater case are some air control flaps and plastic diverter pieces. The larger flaps have a rubber seal at their outer edges. The 2 small flaps have a thin (1/8" or so) layer of foam glued to them. In the pictures, the foam is crumbling and has partially fallen off.
Heater cores for A/C cars are different than the non A/C version. The A/C core is 2.5 inches thick. Some vendors sell a core that is only about 2" thick (a Camaro version?) and is too small for the mounting brackets.