There are several kinds of free-to-play business models. The most common is based on the freemium software model, in which users are granted access to a fully functional game but are incentivised to pay microtransactions to access additional content or more powerful in-game assets.
I think the term is freemium.
Nope, it’s free-to-play
From the article you linked
Dude, the wikipedia-article is called Free-to-play. The preamble even says