Free To Play
A Free to Play game can be downloaded for free and only additional content has to be paid for. These games can mostly be "finished" without paying anything at all, but this might be extremely difficult; however, there are also some games that can only be completed by purchasing upgrades.
An example for a Free to Play game is Lara Croft: Relic Run. It can be downloaded free of charge from the respective stores for all major mobile platforms. With patience all levels can be played and all secrets can be found, however it is far more easy to buy additional Gems, one of the in game currencies, with real world money in order to upgrade Lara's Outfits and Weapons to complete the game faster.