Free: Games that don't cost anything to download, and don't have the option to spend money in game. Free to Play: Games that don't cost anything, but you can spend money in game. Paid: Games that cost money to download, and you may or may not spend money in game (usually you don't.) Before mobile gaming hit it big (I think mobile gaming is only going to get more popular) games were pretty much paid. Mobile changed all that. I personally hate the FTP games, as the true cost of the game is hidden. When you first download it, you have no idea the potential cost. Some are unplayable if you spend money. Free doesn't offer the best games, but it's the best bang for the buck.
Free to play games exist on PC years ago, though, and most of us know that FTP games are often not what they appear. In-App transactions are how companies get paid for the games that they release for free. Free might be the cheapest option, but that doesn't mean it's the most valuable for each gamers. If a person is willing to pay for the experience, and a paid game goes above expectation, then that has far more value than a free game.