A person's level is directly related to their natural ability and the amount of time they put into learning new skills.
The more time you put in the faster you can learn new skills the faster you move up in level.
These timelines are all very loose because someone who is driven and practices every day is going to evolve faster than someone who is casually practicing only once or twice a week.
A beginning student is someone who has put in a year or less on their instrument.
An intermediate student is 1-3 years
An advanced student has been playing seriously for over 3-5 years.
A professional someone who is already playing with other instrumentalists and gigging.