It's both - there's an Imperial Remnant - which fled into the Unknown Regions immediately after the Battle of Jakku, having gotten the location of Palpatine's secret Superweapon Test Site - the future Starkiller Base. (Source - Newcanon Complete Locations)

On getting there, they began the Starkiller Project - making over that small planet, into Starkiller Base.

Some 30 years later, the creation of Starkiller Base is complete.

However - that's not the only thing they're up to.

They send agents into New Republic space, to recruit politicians, criminals, and so forth, to their cause (source (Bloodline)

Some 20+ years after the Battle of Jakku, there is a schism in New Republic politics - and certain "Populist" worlds break away and start calling themselves the First Order - having been primed to do this by the Unknown Regions First Order's agents (- logical extrapolation from Bloodline, the TFA Visual Dictionary, the Propaganda book previews)

But the real heartland of the faction, is not in the "republic breakaway worlds" but in the Unknown Regions, where the Starkiller is, where secret factories are building warships (the Resurgent-class battlecruiser) and so forth.

FO was started by a Breakaway Imperial Remnant who fled to the UR. FO is not the Empire, it's a resurgence group comprised of breakaways, imperial veterans, and fanboys.

Not surprisingly, still less original than Krennel, Zsinj, or Daala.