What's the difference between a Great House and a faction?

They get confused because both evoke a "side", but they play completely different roles:

Great House:

• Cosmetic only — visual identity, banner, Game of Thrones flavor
• No effect on combat, territory or objectives
• Doesn't decide who you fight

Faction:

• One of the 3 real camps (North / Central / South) on the Reign's map
• Drives the territory war: your opponents, your Faction objectives, your faction leaderboard
• Changes every season and isn't a guaranteed choice (balancing)

In short: your Great House is your look, your faction is your battlefield side for the season. Picking a Targaryen or Stark Great House puts you in no particular faction and gives you no bonus. For strategy, what counts is your faction (this Reign's stake) and above all your alliance (your permanent group) — not your Great House.