Free to play games can come in a number of different forms. Some of them simply offer you optional micro-transactions for cosmetic items, and allow you to play the game unfettered. Some F2P titles, which I refer to as "pay to win", allow players to buy non-cosmetic enhancements that significantly boost their abilities, sometimes beyond the confines of the game.
Others, which are arguably the worst kind, are "pay to play": Mobile Suit Gundam: Battle Operation, releasing in Japan for the PS3, is one of those games. Every 24 hours, you can play 12 missions -- after that, you have to pay money to play more, or just wait until your units recharge (according to Siliconera, the cheapest package is 27 units for 1,850 yen, which is roughly a third of the cost of a US retail game). The game also incorporates some pay to win elements, allowing you to unlock every suit, weapon, and part for a price.
Funnily enough, Siliconera is reporting that characters in the game will send you messages begging you to rescue/assist them -- enticing you to pay to come back and play -- a tactic many MMOs have been using for years. Come June 28th if you have a Japanese PSN account, definitely give it a try. On paper it sounds rough, but if you have the mental fortitude to limit yourself below the daily allotted mission count, it could end up being pretty awesome -- just don't get addicted.