Shore A scale is for testing the following materials:

Rubber: Soft vulcanized (ie tyre), natural nitrile
Elastomeretric materials (rubber & rubber like): GR-S, GR-1, neopene, thiokol, flexible polyacrylic esters neoprene, thiokol, flexible polyacrilic esters.
Other: Wax, felt, leather etc. (materials that normally yield under fingernail pressure, such as the heel on your shoe).

Shore D scale is for testing the following materials:

Rubber: Hard
Plastics: Harder grades such as rigid thermoplastics, plexiglass, thermoploystrene, vinyl, sheet, cellulode acetate, thermosetting
Laminates (ie fornica) 
Other: Paper filled calendar rolls, calendar bowls, etc. (materials that would not normally indent under fingernail pressure, such as a pocket comb or bowling ball).