Can people in western countries do graduation and post graduation in two completely different fields? It might be possible here in India too, I haven't researched on it, but in one movie I have seen the guy is studying mathematics in MIT but his future plan was to study medicine at Harvard. I kept wondering how could he do that.

Here at India at 11th class we have to usually choose either Mathematics or Biology and then our eligibility changes accordingly.
Some universities require students to have similar bachelors degree, some other do not require similar degree and do not have specific policy on this; while others need a related or so near bachelors field. For instance, for a masters in engineering degrees; one with bachelors in applied mathematics or physics will also be able to study masters of an engineering field.

Answers to your question varies in fields and countries, and different education systems. My general advice to you would be to see the minimum requirements of the university you want to apply for to see whether their admissions office have any regulations on having related bachelors degree to the masters or not. If they are not providing you information on this, I recommend you to contact them by email and ask your questions.