Typically, people do associate the terms with different forms of power, but they’re really the same thing. A motor creates motion using supplied power. That’s what a car engine does: it uses the chemical energy in fuel to move pistons.
If I understand correctly about your line of work, this is consistent: the supplied power source is converted to rotational motion in the fans. Your compressor engine is also a motor.
If you have something else that turns the airflow into electricity, then you have a generator there, and will need another motor to make stuff move again.
This is also why hybrids need an electric motor and a gas engine: they have a generator that turns motion into electricity, so they need something that turns electricity back into motion.