Identification: what kind of fruit tree is this?

So I recently moved and my new backyard has apricot, avocado, pear, and lemon trees. The last one I'm not sure of. I attached photos. At first, the fruit was fuzzy but then lost its fuzz and started changing color. I also found a ton of old pits surrounding the tree. My first guess was peach, but now I'm not sure.

 

Nectarine?

 

It looks like a Nectarine to me, too.