go in much more depth. A fellowship is basically a gift (from the university or some outside agency) to support your graduate studies. Before you can get a PhD, you'll need to complete your prerequisite education and take the GRE, or Graduate Record Exam. As the latter are often missing nuclear weapons essay css forum or weak, the former tend to be missing or weak as well).
A "post-doc" is just a non-tenured fixed-term research position which requires the maturity and experience which. PhD support is of three types: Teaching assistantship. There isn't really such a thing as a "post-doc". At least in the US, each of these kinds of support usually comes with payment of tuition or a tuition waiver, which can be comparable in value to the stipend. For example, I was half teaching assistant and half research assistant when I started my graduate studies. Thus in many countries there's a glut of post-doc positions and a dearth of proper academic staff positions. Ideally, the professor is your thesis advisor and the work you do relates to your dissertation, but that isn't guaranteed. The thing is, non-tenure-track researchers are cheaper, and require less commitment. It should really be referred to as the "normal track" for employment of academics. Apart from these three kinds of support, there might be options for on-campus employment outside the department, but that is usually at an hourly rate with no tuition benefit.