"Any stacked units in adjacent lands are removed"
In one given stack, are both units removed or only one ?
I read it as only one unit is removed. Much like a single unit in an adjacent region is ignored, all this is doing is removing the 2nd unit.
"Conquer one land for 1 unit only"
Is this "payed" unit the unit which is placed in the land or another one ?
It is the unit you place in the region. Instead of rolling (or using diceless combat), it is a single automatic victory.
What is exactly the difference with Assault ?
This can count towards accomplishing a kingdom Advance whereas Assault cannot.