Question: I am a PhD student in Mathematics. I wanted to know what exactly is the difference between PhD and Postdoc. Is it just the research that one does after PhD(kind of second PhD?)?

Answer: 
I want to address this question by citing my current Master's advisor when I asked him the same question:

1. In the Bachelor's, you learn the basics of the area.
2. In the Master's, you learn what people are doing in the field and how to read scientific papers.
3. As a PhD, you learn how to develop your own research and start having new ideas on the field.
4. As a Post-Doc, you learn how to mentor other people's research while producing your own work without supervision.
5. When you reach Professorship you only have to look smart!
A postdoc is expected to know what they are doing, and to be productive researchers with minimal supervision. PhD students are learning how to be researchers: by the end of the process, they should be on par with a postdoc, but it will take time to get there

Edit: This comment has been copied from Barbara Robson's answer [here](https://www.quora.com/What-are-the-main-differences-between-post-doctoral-research-and-Ph-D-research).