>>1215673 #Thinning will effect fruit size, but pruning won't. If you neighbour hasn't been thinning the the difference is probably just down to the genetics of the tree. A lot of crab apples have DNA from wildling and 'escaped' domestic apples and the fruit size can massively vary due to this.
Definitely do some reading on pruning, if you don't know what you're doing it can do more harm than good. Also try to find out what apple tree you have! Different varieties can need quite different treatment, have very different growth habits, disease resistance and either be spur bearing, partial tip bearing or fully tip bearing, which will have a massive impact on how you should approach the task of pruning.
>pic related: one of the wildling apples on my land 