Online games are simply games that requires one setting up an internet connection before it can work while the offline game is one where you don't need any internet connection to play. Do you play more of one than the other?
I like to have both online and offline games on my phone so that I have the ability to play them whether I have an internet connection or not. I would say that I do play more online games though when I do have an internet connection, I just have the offline ones there for when I may need them.
I will pick the offline games. I wouldn't want to play a lot of online games that will mean using internet subscription. That is not something that I would always want to do.