Alliance vs faction: what's the difference?

It's a common mix-up, but the two have nothing to do with each other:

Alliance = your chosen group of players (your guild).

• Persists across reigns and world merges
• You pick it / join it / build it
• Used to coordinate, climb the alliance ranking, earn Heirloom currencies

Faction = the side you're assigned out of 3 on the map (North / Center / South).

• Reshuffled every season, balanced by the game, not guaranteed
• Defines who you fight for territory during that reign
• Disappears at the end of the reign

In short: the faction is temporary and imposed (the season's framework), the alliance is lasting and chosen (your real group). If you want to play with friends over time, put everything into the alliance — you'll stay together even if you end up in different factions next reign.