Actually it's more like they're both.

But that still leaves one question—was the party an actual party, or were they merely symbols meant to represent you, the players? Well, you can breathe easy knowing they are both. They all ventured into Eorzea at the same time as you did. They all did similar quests, and lived through similar adventures. They exist as your characters exist (in a virtual world-sort of existence). The fact that you haven’t come across them is probably the same reason you haven’t come across my character, Amanda Hugginkyss (or maybe you have? /wink). They’re just somewhere else. Though, maybe you’ll stumble across their party in the future. Or maybe you won’t. How’s that for committing to an answer?
Bolded part is what I'm looking forward to as a possibility.

It'd be neat. For promotional material they'd be just symbols, but ingame they could be actual characters doing their own thing apart from our quests.