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 have always understood a postdoc to be a "post doctoral" position, that is a paid post. The idea of a postdoc position is to do research roughly in the area of the PhD, with the person gaining experience that would possibly be of help in gaining a full time position.
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).