No, compliments and badges are not the same.
You can earn badges by performing different actions on the site. There are 3 types of badges, Socializer, Party Starter and Networker. Each of them has 6 levels, from Rookie to Jedi, and you go up the levels the more you attend and create socials or add friends to your network.
Compliments are given to you by other members after you attend a social together. There are 9 types of compliments and they are chosen by the person who gives them to you.