Looking for information and help identifying two apple trees.

Hi, moved house last year and found two apple trees at the back of the garden. They have suffered years of being smothered by fir trees which I cut down not long after I moved in. They do seem to have a new lease of life since getting more light although their trunks and branches remain covered in a mossy type of growth. The tree with the green apples has lost a number of its fruit at different stages of growth but the leaves are looking good. The tree with the red apples hasn't lost as many fruits and has a big crop which appears to be nearing maturity, but overall the tree doesn't look as healthy. Both have produced some fruits that appear to have bad spots on them. I have no experience of apple trees but I know these definitely need some TLC and I would really welcome any information that can help me identify them and any tips on how to revive them as much as possible..
Thanks in advance..

 

I would say they are both cooking apples.