Difference between mobile site and web responsive? What should be the approach?

There are so many sites that work on m-site particularly like makemytrip but one the same side, there are products that are web responsive which are manipulated using the CSS media queries.

One of the reasons that I know is to make the native apps for the android, and iOS using frameworks but I am not very much convinced with this solution.

I want to know the usability and the approach to making the m-site of the product. Are there any principles or set of requirements that you should meet before proceeding in making a dedicated mobile site.