I'm just as unsure as you are.
It makes sense for it to be the "Load/Push vehicle labour, but the way loading jobs get picked up is erratic at best.
Ill explain: In my last fort I'm using quantum minecart stockpiling for wood and stone, with several small 6-tile stockpile set up to giving to a cart stationed on a stop dumping into a 1-tile stockpile.
In other words, the standard minecart quantum stockpile.
While lazily observing these stockpiles not bothering with other more important problems such as the zombies locked outside, I've seen that the way hauled items are handled is very strange.
I've had dwarves come to the stockpile, pick up a wheelbarrow, grab a stone from the quarry, bring it back to the small stockpile where they immediately drop the wheelbarrow, load the stone into the cart and pick back up the wheelbarrow, for maximum efficency hauling.
More often than not, dwarves only do a part of the hauling job, the other parts being claimed by other idle dwarves. For instance, a dwarf will haul the stone to the stockpile with the wheelbarrow, but the go idle as another dwarf will load the stone in the cart and another one picks up the wheelbarrow to grab more stone.
Occasionally dwarves fill the 6 tile stockpile to full, with nobody caring about loading the cart, then a random but usually short time later someone does start to load the cart. Sometimes it's a single dwarf loading each of the 6 stone one after another, sometimes it's 6 different dwarves acting one after another, sometimes it's a flash mob of 6 dwarves rushing in all together.
During the whole time the 6 tile stockpile is full and no load jobs are generated, the cart is empty and ready to be loaded.
It seems that the game handles load jobs differently than hauling jobs, as they sometimes end up "desynchronized".