1. Is plaster and lath gypsum based? In my experience plaster is basically identical to stucco, which is basically just mortar with increasingly fine sand. It is very hard and completely unlike drywall.
2) Why emphasize asbestos when talking about plaster? My understanding is you likely have more to worry about if you have a house from say the 40s-70s, which almost universally have some sort of drywall product.
We had our circa-1915 house checked for asbestos before lifting it. The inspector laughed after taking a chip out of the plaster because you could clearly see horse hair protruding from every side of the chip. This is apparently unlikely to overlap with asbestos, though it comes instead with a minor (?) anthrax risk. I'll take that over the dust from drywall sanding every time though.
"Plaster" can be lime, gypsum, or cement, in rough order of historical adoption. Sometimes you even use different types on the same wall; cement rough coat and lime or gypsum top coat, for example.