1. Postdocs intended to benefit the postdoc, often with structured professional development programs. Of course, these postdocs are supposed to benefit the research center who get to renew their training grants if the postdocs turn out well, but the key fact is that the postdocs have autonomy and define their own success.
2. Postdocs intended to benefit a faculty member. At one of my first interviews, I was sitting with a senior and a junior faculty member, and I asked what the role of the postdoc was. It was an innocent question, and I wasn't thinking of it in any kind of cynical way. The junior faculty member was a grad school cousin --- their advisor had served on my committee --- so felt almost like a relative. The answer came immediately from the senior faculty member, "To get
After this interview, which fortunately came early, I started looking at all postdocs as structured programs to benefit the postdoc versus to get a promotion for a faculty member, and noticed that all of the posted postdocs could be divided in this way.
In addition, there is a third type of postdoc, which tends not to be posted. That's the kind that I'm in now.
3. The employee postdoc: The postdoc is an employee on a project, like any other employee, and often one of many. They have the title of postdoc, but it's a bit arbitrary because they don't do anything different from the research scientists or other non-PI researchers. Their work benefits the PI, but since they are one of many, the PI does not have such a tight leash on them.