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.
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.