The first Assassin's Creed game was about a conflict between the Nizari Order of Assassins and the Knights Templar, two militant religious orders who were on opposite sides of the Third Crusade*, which makes sense for a game set in the Levant during the Third Crusade.
However, because the devs want to expand this conflict in each of their games, and because they want to explore different time periods and regions of the world, this specific conflict rooted in the historical realities of the Levant during the High and Late Medieval period has been stretched out into this shadow war that has been raging for thousands of years from Japan to Britain to the Caribbean.
It's not a problem, but I think it's been very interesting watching this conflict transform as the story expands to meet the needs of the gameplay. It presents this weird alternate history where the historical Templars and Assassins are just one facet of this ongoing ideological conflict. The historical Knights Templar were named after their fortress on the Temple Mount, but the in-game Templars existed for millennia before that point. It's like that joke of two Roman soldiers wondering what their calendars are counting down to.
