Spent last weekend poking around my folks' place (built 1957) trying to ID the same kind of dark gray fluffy insulation sitting between the joists. Here's what I learned the slow way so you don't have to. First, look at the texture. Rock wool from that era looks like coarse gray-brown fur, kind of chunky and fibrous, often with little specks of shiny material in it. Cellulose looks softer and more papery, gray and dusty, and it settles flat over the years. Vermiculite is the one to watch for, it's pebbly, like little accordion-shaped chips, and it can hold asbestos if it came from the Libby mine.
Since your gray layer sits right down on the ceiling boards with no pebbles under it, that's actually a decent sign it's not vermiculite, but check the bottom layer anyway by gently parting a spot with a flashlight, don't dig around and stir dust up. The white stuff near the chimney is ussually just older fiberglass or rock wool batts that lost thier facing, and the pink paper-backed rolls are obviously fiberglass. If you really want certainty, put a small sample in a zip bag and send it to a lab, costs maybe 30 to 50 bucks. Honestly though, most of that gray loose-fill from the 50s and 60s turns out to be rock wool, and disturbing it is the main risk, so leaving it alone and blowing new insulation on top is the usual play.