Great Question, I use very old HP ipaq's that have ARM processors, I also use energy micro 32bit ARM microprocessor's. So I think of it as a processor core, often used with a mix of different things to turn it into a microprocessor.
Whatever it is, they sure are amazing to use! I have a energy micro 35DK dev board with a ARM32 bit processor.
Some of the demo's that came with it are gobsmacking!! it has a inbuilt energy meter so in real time while running or debugging a program you get a live readout of how much current your using, it goes down into the nA region.
Is realy cool to see some the stuff it can do, ticking along drawing less than 1mA and running at 1% of cpu.