General purpose compressors (as opposed to compressors specifically for airbrushes) typically use one of two sizes; 1/4" NPT or a larger size (3/8" NPT I think but I'm not certain). Airbrush compressors usually do not adhere to this since they will size the outlets to match the hoses for their airbrushes. You can get adapters and fittings for general purpose compressors at most larger harware stores such as Lowes or Home Depot. If you have an airbrush compressor, you are going to have to find adapters that specifically fit that model.
Also, I think that airbrush hoses are not consistant from one company to another. I'm pretty sure that Badger and Paasche are different. Not sure about Iwata.
I understand that the propellant cans are all different. I have an old Badger Propel adapter and I don't think it will fit anything other than Propel cans and Badger hoses. Get a can of Testors propellant and it will probably only fit Aztek hoses and can adapters.