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: 
In mathematics, a "postdoc" is a special kind of faculty job you get just after your Ph.D. It may have a fixed term (not tenure track). It may have reduced teaching, so that you can concentrate on your research. You may have a "mentor" assigned to advise you on doing research.

But (unlike some other fields like experimental physics) you are probably not working in someone else's "lab" on someone else's research program that someone else got the funding for.
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).