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: 
The first and foremost difference between the two is that a PhD is "awarded" after defending a thesis (plus additional duties depending on the department). On the other hand, a PostDoc is a temporary working position that is assigned by some institution, whose completion does not require any defence.

What people do or do not do, researchwise, in their PhD and PostDocs is very much dependent on the area and on the department (you may look at other answers that go more in details on this and that I do not want to overwrite, as I would just copy and paste them).
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).