“Amateur” is from latin “amator”, that means “lover”, “the one who loves”.
“Professional”, which has the same root of “profession”, is from latin “profiteri”, that means “declare publicly”, and it has for a long time denoted the vow made on entering a religious order.
The difference between amateur and professional is in their roots.
An amateur is somebody who loves something and likes to practice it.
A professional, on the other hand, is somebody who is deeply passionate about something, so much so they devote their life to it.
You can do things as an amateur (many things, possibly) or as a professional (few things, probably). The difference is in the amount of effort and work you put into it.