The word can refer to a few things. It can refer to the fruit, or to an artificial flavour, which has little to nothing to do with the fruit, as it tastes nothing like the fruit. It also has a euphemistic meaning which I won't go into.
In terms of sour cherries, I can only assume that 'cherry' refers to those fruit too, based on the name. I can't be completely sure as I've never seen or tasted one.
We have cherry blossom trees here, and we do refer to their fruit as cherries, even though they are too small to bother eating.