So you want to do science for a living. Some scientists work for companies, developing new products. Some work for governments. But if you want to do “pure science”, science just to learn about the world, then you’ll likely work at a university, as part of what we call academia.
The first step towards academia is graduate school. In the US, this means getting a PhD.
(Master’s degrees, at least in the US, have a different purpose. Most are “terminal Master’s”, designed to be your last degree. With a terminal Master’s, you can be a technician in a lab, but you won’t get farther down this path. In the US you don’t need a Master’s before you apply for a PhD program, and having one is usually a waste of time: PhD programs will make you re-take most of the same classes.)
Once you have a PhD, it’s time to get a job! Often, your first job after graduate school is a postdoc. Postdocs are short-term jobs, usually one to three years long. Some people are lucky enough to go to the next stage quickly, others have more postdoc jobs first. These jobs will take you all over the world, everywhere people with your specialty work. Sometimes these jobs involve teaching, but more often you just do scientific research.
In the US system, If everything goes well, eventually you get a tenure-track job. These jobs involve both teaching and research. You get to train PhD students, hire postdocs, and in general start acting like a proper professor. This stage lasts around seven years, while the university evaluates you. If they decide you’re not worth it then typically you’ll have to leave to apply for another job in another university. If they like you though, you get tenure.
Tenure is the first time as an academic scientist that you aren’t on a short-term contract. Your job is more permanent than most, you have extra protection from being fired that most people don’t. While you can’t just let everything slide, you have freedom to make more of your own decisions.
A tenured job can last until retirement, when you become an emeritus professor. Emeritus professors are retired but still do some of the work they did as professors. They’re paid out of their pension instead of a university salary, but they still sometimes teach or do research, and they usually still have an office. The university can hire someone new, and the cycle continues.
This isn’t the only path scientists take. Some work in a national lab instead. These don’t usually involve teaching duties, and the path to a permanent job is a bit different. Some get teaching jobs instead of research professorships. These teaching jobs are usually not permanent, instead universities are hiring more and more adjunct faculty who have to string together temporary contracts to make a precarious living.
I’ve mostly focused on the US system here. Europe is a bit different: Master’s degrees are a real part of the system, tenure-track doesn’t really exist, and adjunct faculty don’t always either. Some particular countries, like Germany, have their own quite complicated systems, other countries fall in between.