What is the theory behind fans and blowers?

If you are asking not about how they are used, but about how they work, that is called fluid dynamics. See https://en.wikipedia.org/wiki/Fluid_dynamics
See also https://en.wikipedia.org/wiki/Lift_%28force%29 and https://en.wikipedia.org/wiki/Bernoulli's_principle
A fan or blower operates by transferring momentum from the blade to the fluid [air]. It transfers energy as well, but it is Conservation of Momentum you use to solve, not C of E.

Fluid dynamics for Chem Engrs are [or at least were] taught combined with heat transfer and mixing/diffusion in one course, because at they basic level they are all mathematically very similar. Also because the transport of mass, momentum, and energy all affect each other in nonlinear ways.

THEY ARE THE SAME THING.....
RUN WITH MOTOR.
BLOWER HAS HIGHER SPEED, MORE BLOWING FORCE, CONSUME MORE ELECTRICITY AND QUITE NOISY.
FAN JUST HAS THE OPPOSITE PERFORMANCE FROM ABOVE.

turn a propeller or blower using any kind of motor. Propeller or blower create positive pressure to move air.