>>1215673Thinning 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. If you look at the blossom, some is produced on spur systems but much is at the tips of last year's New growth. This is a partial tip bearer and normal pruning of this tree would massively reduce blossom and subsequently fruit.
I grow apples on their own roots, but I use M26 nurse roots and plant deep so the soil level is above the graft union as I've found this has a greater success rate than rooting the cuttings directly. Actually using directly rooted cuttings I couldn't produce trees lasting more than 6 months. Definitely report back on your results.