Oh man I am too used to pathfinder
Full attack actions on the move? What is this sorcery?
It's weird from a 3.5e perspective too... Also, it's completely fluid! With a speed of 30ft and 3 attacks, you can distribute those attacks however you choose in during those 30ft of movement. You could move 10 feet, attack twice, then move another 20 and attack the third time.
http://5e.d20srd.org/srd/combat/movementandPosition.htm(Sorry Mathel)
So everyone basically has the spring/flyby attack feats, except even more powerful. Not to mention getting all attacks every round despite moving more than 5ft. It's... interesting, it was sometimes difficult to pull off a full attack in 3.5e when people kept moving away. Of course, there were many solutions.
Anyway there *is* no move action, anymore. In fact there are ONLY standard actions, period! Normally just one per round, though the fighter can "action surge" for 1 or 2 extra (between short rests).
A "dash" action adds your base speed to your speed for the round... Essentially like a "double move" in 3.5 would be, though you can stack more on with action surges.
Hiding is just an action, so I see no reason a fighter can't move their full speed to an enemy... hide... then use an action surge to sneak attack.
Full attacking is also a repeatable action, which is how you get 12 attacks in a round (amidst moving your base speed, and using up 2 action surges on full-attack actions).
I guess I can see it working, it's just much more generous to melee than 3.5e is. About time maybe, heh... Scary though.
Edit: Returning to the original question, though, there's really no equivalent of running. "Dashing" is equivalent to using both move actions to hustle in 3.5e, moving you at double speed. Running for 3x-5x speed, for up to a minute or 2, if you aren't fatigued? That's just not a thing. A top-level fighter can use up both healing surges to dash three times in a round, for 4x speed, but that's ONE round before they need to recharge with a rest.