If you have a gage, bullace or damson in front of you, then you also have a plum in front of you.

I don't think "gage" is a valid separate category, rather a vague term for a group of certain small roundish plums.

Damson is a subspecies of plums, specifically Prunus domestica subsp. institia.

But many of the "damsons" we grow are not subsp. institia, rather they are plums which have been bred to be like damsons. Rather like John Downie, the most popular variety of "crab apple", is actually just a variety of "eating apple" Malus domestica. Though species crab apples are also available.

My understanding of "bullace" is that it means something that is a wild damson, or close to it. But again, it is not used in a consistent way, and may just refer to a variety that is more like a wild one.