Pure math is just math for the sake of it, whereas applied math is math which has real world applications. However, some topics which were previously pure now have real world applications (e.g. number theory in cryptography), so the line between the 2 classifications can be blurred.
So, I have been looking into college courses to see what I want my major to be, and I noticed that M.I.T offers two specified types of Mathematics. Pure and Applied. What is the major differences i...
math.stackexchange.com
Here's a (somewhat) helpful video (I don't agree with some parts of the video, where they classify certain applied topics as pure, but its a helpful video nonetheless):