Not all states have a formal system, but some do. An apprentice is a new trainee, possibly some classroom training under his belt, possibly he works as an apprentice during the day and classes at night. An apprentice is not supposed to work unsupervised. In some states, there has to be one journeyman for each apprentice on the job.
The journeyman level in most areas calls for a minimum 5 years on the job, followed by an exam which may be just written, on code and other issues, and in some states also requires performance of actual tasks, like leading or soldering.
Then, in some states, there is the Master Plumber cagtegory. After several years as journeyman, you take more tests. A Master Plumber can own a business and employ journeymen and apprentices.
These terms also are used within the trade union system , if you are a union member.
Then there is California. No licenses for apprentices, journeymen, master. If you can show somehow that you have worked for 5 years, then you take a written test, which is not too strenuous, and get a Plumbing Contactor's License. With this, you can own a business, pull permits, employ anyone you feel like, and send them out to unsuspecting customers.