Events are game industry events organized according to their main theme in the industry. Do they cater to developers more than the general public? They may be Conferences then, or possibly Summits. Do they have large showfloors and are geared toward product demonstrations? They may be conventions. Are they open to the public and often have contests and other fun themes? They will likely fit in the Fan Event category then.
PAX Prime or Penny Arcade Expo is a festival for gamers to celebrate gaming culture that focuses on computer and board games. The first international PAX was held in Melbourne, Australia in 2013. There is also PAX East and PAX South events.