Apple doesn't use ARM cores. They have a license of the instruction set that they use to develop their own cores, so technically they aren't ARM cores, but Apple cores that are using ARM instruction set.
Arm designs cores that are being used in processors. Those are therefore Arm based processors. Apple is one of a very few companies that have a license to develop their own cores using the Arm instruction set, i.e., their cores are Apple cores and therefore their processors Apple processors.