There have been some posts regarding what I describe in the title, but none seem to understand what the aim is. So I'll try to described it further here:
I want to take an image, which has in it black, various increasingly light grays, all the way to white, in a complex arrangement (essentially a grayscale image). With that image, I want to re-define it so that the black is transparent and white is opaque, with the grays between representing partially transparent, with the ones closest to white the least transparent. I think you have the idea by now.
I then want to use that to be a mask that sits on top of another layer. So, for example, that mask on top of a solid colour of red would then look like the same original image, but instead of the black, with grays and white, it would look red where black was, then increasingly lighter reds until where white was in the original remains white here, with very light pinks near it, representing the very light grays.
Sounds like it should be really straightforward, and the sort of thing Photoshop is designed for, but no explanation of it so far has laid out in clear, simple steps, how to do this.