Arena PvP is an equalized style of PvP available in 1 on 1, or as 3 on 3. 6v6 PvP is a non-equalized type of PvP where 6 players must fight the opposing team and hold capture points. Open World PvP can be done anywhere but is usually done as Faction PvP.
For open world PvP, players can fight any other players when they wear the appropriate outfit to make them "enemies". These are the matching pairs of faction-related outfits. A match means they can fight one another.
Cerulean Order VS Crimson Legion
Bamboo Guard VS Blackram
Skyhaven vs Talus Dominion
Stratus vs. Tyrian Cult