There are many different types of jobs in Germany. The biggest difference is between jobs where you are employed by someone and jobs that you are doing on your own: then you are self-employed.
Furthermore there is unlimited and limited employment. Unlimited employment is quite rare. The more usual case are limited contracts that end after a certain period of time. And if you do not get a new contract after the old one ends you end up being unemployed. Except for the time limit these types of jobs are the same.
Apart from that there are part-time jobs or temporary employment (Zeitarbeit).
An Ausbildung (apprenticeship) is something different. You will get paid by your employer, but you are still in the educational process at the same time. You spend three years in a company that gives you the opportunity to collect practical experience while you go to school as well. It is a good option for people that do not want to go to university because they want to do something related to practice. In the end you will usually earn more money when you finished an apprenticeship in comparison to people without a specific job-related education.