MMORPGs today use a wide range of business models, from free of charge, free with microtransactions, advertise funded, to various kinds of payment plans. This list uses the following terms.
Free-to-play (F2P) means that there is no cost to purchase the software and there is no subscription charge. Variably applies to traditionally bought and forever available games (see Buy-to-play below). Most newer MMOs that fall under this category now includes microtransactions however, which causes them to overlap with the Freemium model.
Freemium means that the majority or all of the game's content is available for free but players can pay for extra content, character customization, added perks or faster advancement into the game via microtransactions.
Buy-to-play (B2P) means that the MMO can only be played by purchasing the game, but there is no subsequent subscription fee for playing the game. These games may or may not include additional microtransactions, or may sell additional content in the form of expansions instead of asking for an ongoing subscription fee.
Pay-to-play (P2P) means that the MMO requires a monthly subscription fee or other ongoing fee in order to continue playing the game. It may also require an up-front purchase of the game in addition to the monthly subscription fee, though many of these up-front purchases include a month of game time. This was once the most common way for MMOs to finance themselves, but has fallen out of favor in recent years as an increasing number of games have switched to other business models due to difficulty in retaining a stable playerbase.