There's a tree in our yard of which we do not know it's name. In other parts of the yard it grows more like a bush. It has thorns and grows small solid fruits that turn dark blue when ripe. On the picture attached one fruit still looks green. Question is: what is our tree-bush's sort?
I suspect it may be Prunus spinosa, commonly known as Sloe - should have had creamy white flowers in Spring, and does have stiff, thorny branches. If left unpruned will reach about 16 feet in height, but is often seen as a bush or shrub. If it is, and you drink gin, time to make sloe gin! More info here
It looks to me like a plum tree—probably a dwarf. It's possibly a Stanley prune plum, or a similar variety. We've had plum trees and I've seen several besides, and that's what it looks like to me, based on the close-up picture with the small branch and fruit.
Bamboo's suspicion sounds like a good one to me, though.