PF*, 3e, 3.5e, 4e are all editions of Dungeons & Dragons, the big kahuna of RPGs, the one that started it all in 1974 and remains the most popular.
D&D does medieval-esque fantasy roleplaying with a particular focus on killing monsters and taking their shiny gold. The specific rules vary quite a bit between editions. The latest edition is 4th, released 2008. It has had a polarizing reception among D&D fans and they're working on the next edition now, asking for all D&D fans to come together and contribute to an open playtest to get everyone back on the same page. That's what the "New Horizons" subforum on this site is about.
* Actually PF refers to Pathfinder, a game created by a different company than that which currently owns and publishes D&D as a sort of "clone" of edition 3.5, where they use the same rules but change around some names and concepts to prevent copyright infringement. It competes with the official 4th edition. It counts as D&D, it just has a different name. There are also "clones" of really old editions, going back to '80s era Basic and Advanced D&D. Swords & Wizardry is a clone of original 1974 D&D, Labyrinth Lord is a clone of 1981 Basic D&D, OSRIC is a clone of 1979 Advanced D&D. The clones mean we have all editions in print now. Actually except for second edition...is there a 2e clone yet? Not sure.
There are many, many, many other RPGs besides D&D. In fact I think there are too many, and that this is a primary reason why the hobby is intimidating to get into. If I were you I would just start with D&D and not bother looking into anything else just yet, since you said you are into the fantasy genre.