Although ARM 7 (LPC2148) and ARM cortex-m series is controller. But when someone asks about ARM, we use the word Processor not controller why??
Personally I prefer that it is a processor, and not a controller
A microcontroller has a microprocessor built-in.
It's like computers have CPUs (Central Processing Units). A CPU is not "the harddisk" or "the cabinet" as modern people start to call them. The CPU is the chip that's runs the software and is connected to the RAM and peripherals via bridges.