An evening with Google finds that real gutta percha is made from the latex of particular trees native to Malaysia. It is thermoplastic and can be heated and molded to shape.

Hard rubber is made by heavy vulcanization of India rubber which is based on the latex of different trees.

One article said that gutta percha is not brittle, while we know that old black grips are very brittle. Which makes them likely to be true hard rubber, Colt advertising of the day notwithstanding.