There are generally two ways to create a dwarf apple tree. One way is to specially breed them smaller.
This is very hard to do and may take hundreds of years.
A faster, and much more common way is to graft the tree onto a rootstock that has been selected for its dwarfing characteristics. There are several different types of rootstock, and each works best with specific trees.
Dwarf apple trees often require much less care than full sized apple trees.
The rootstock chosen for the dwarf apple tree will often be much hardier than the original root system of the tree. Also, the smaller stature of a dwarf apple tree will mean that less pruning needs to be done, and the tree will require less spraying. Less tree to care for means less work to do.
Just about every breed of apple tree can be dwarfed. The type of the dwarf apple tree depends on the variety grafted, while the size depends on the rootstock used.
Some rootstock will dwarf apple trees more than others. It is important to select not only the breed of tree desired, but also the size. A dwarf apple tree will grow better in a home garden than will a full sized apple tree.