Processor or controller?

am confused. whether arm is an processor or controller.? if it is a processor then why is it called so? while we talk about embedded sys we say that emb sys is one which performs single action/job/task. 8051 performs single task. 8051 is controller, we cannot dump more than one source code or make to perform more than 1 task. whereas our CPU(in personal computer) has processor and we can dump/ install new software to that. its a processor and not controller hence it won't come under embedded(only if we consider entire system/PC..if we consider only mouse/KB/monitor then it comes under emb sys because it performs single task). even arm is a PROCESSOR then how come it comes under emb sys?