Firmware is software that is specific to its hardware. It is directly configuring/operating the peripherals through their registers.

An embedded device is the alternative to a general purpose computer such as a smartphone or laptop. The users of general purpose computers can decide which applications get run, unlike embedded devices. Of course, other software can limit the user's ability to make those decisions, but that is not an inherent limit of the system, that is an artificial limitation imposed by another person.