Here is a pic of the tree itself.

Pictures of the buds aren't too great.....those are leftover fruit from last year. I never noticed fruit before and I didn't actually get to see it last summer. When I break open the fruit it only has one seed inside. The seed resembles an apple seed but of course it sits in the center and thereis only one. It has a couple mullberries on one side and a couple of unknown variety apples on the other, all planted by someone else quite awhile ago.

Jag,

The tree in the photo probably a flowering pear. You can graft any pears to it and not cherry.

Tony

I'd assume Tony is right, but if you have any doubt open up one of those leftover fruits and see if there are seeds or a pit in it.

Please prune those stubs out just leaving the tiniest bit past the branch collar. They are killing me.