Disease on apple tree

We have two 10 feet tall apple trees about 10 feet apart. This is a house we moved in to in January, so I don't know the variety. One of them has thrived with lots of leaves, flowers and now lots of budding apples. The other seemed to struggle with only a few flowers and now a few apples appearing. On the struggling tree, I can now see patches of white fluffy powder on the branches and bark, anywhere that it has been pruned, or where twigs have broken away. The leaves and fruit seem unaffected. Also, there are a couple of patches on the main trunk of something that looks like dark fur.

I have seen references to powdery mildew or insect infestation but was under the impression this affects fruit and leaves?

Is this something I can treat and is there a danger that this will spread to the healthy tree?

Many thanks.

Andy