Embedded means bare metal access to everything. An OS like Linux shields such functionality, which is why it's frustrating to implement something as simple as a triac dimmer in a Linux SoC without doing everything in kernelspace to avoid kernel jitter and event delays.

Embedded systems typically run on a microcontroller. It almost literally means something that reads an input from the physical world (EXTI, logic level or adc) and uses it to control something. Microprocessors typically implement a bus system and additional units like an MMU. We used to have uC with basic busses, but that was for different reasons (EPROM, LCD, ...)

These days the word embedded seems to mean "fits in a small box".