Technically: There is none. Both are radio, they both use the same technology. The difference is in regulation.
Ham radio is designed for hobbyists and experimentation. Cell phones, wireless internet were both done over ham radio first. Even radio itself all started out as hobby experimentation.
Depending on what you mean by common.
Ham radio is a licensed two-way system. We have access to sections of the radio spectrum from just above AM radio at 1.6Mhz, all the way up to several Gigahertz. Different frequencies have different properties. Higher frequencies are good for high quality short range communication, and digital (computer) communication. Lower frequencies are typically better for longer range communication (global), but at lower quality and not very good for most digital uses.
Common radio: If you mean things like CB, FRS radio, and toy walkie talkies, all of those services have very heavy regulation and very low power limits. Commercial radio (like FM stereo and AM radio), are one way communication. You can't talk back to the DJ. With Ham radio, you can't do anything commercial, and you must have a license, which involves passing a written test on basic regulation and theory. Once you pass this test, you can run up to 1500 watts on some frequencies (in the USA), vs 4 watts for CB or 0.5 watts for FRS radios.