The current crop of "enduro" bikes were, I suppose, born out of what was termed "all-mountain" bikes - bikes that were able to tackle as wide a range of terrain as possible; built burly enough for everything short of World Cup downhill courses but still able to be pedalled uphill on all-day big-mountain rides. My Specialized Pitch Pro is probably a typical example (in stock form): 150mm travel front&rear, slack(ish) angles for stability on testing terrain, big rotors, wide bars, 2x9 drivetrain.
Since Enduro has become a serious competition series (see the EWS), enduro bikes have taken this a step further with 1x drivetrains reducing the chance of dropping a chain when going for it on a stage, dropper posts to keep flow and momentum on undulating stages, and so on.
They are immensely capable, and better than you'd think at getting uphill, but a proper enduro race bike would be compromised as a true all-rounder given that its primary aim is to descend as fast as possible at the expense of climbing efficiency between stages. Call it the "winch and plummet" effect, if you will. They seem to be the fastest growing sector though, so there's obviously something in it.
Dan Atherton nailing Stage 5 of the Enduro World Series in Whistler; witness his speed at 4m15s onwards!
https://www.youtube.com/watch?v=StPeEgz5Cfo
PS. The Ghost ASX is a trail bike. From the 2013 range, the enduro bike would be the Cagua/650B
