Aerosol sprays of any kind are liquid particles (like paint droplets), suspended in a gas "propellant". However, the gas isn't a gas while it's inside the can. If you just filled a can with compressed air, it would be very dangerous and it wouldn't last long.
Aerosol cans are filled with a substance that is a liquid in the high-pressure environment of the can, but that also easily evaporates when it is allowed to escape the can.
You are correct, this is an example of diffusion. It's just important to understand that it is not pressurized gas inside the can.