Curraghs cannot carry any troops. Galleys can.
One advantage of using the (L)oad key is that it preserves the unit's movement points. This is not ususally very important until the distance you want to ship the unit is small, like one or two tiles or so. If a units just moves onto a ship that is in a coastal tile, it uses up all of its movement; if the ship sailed to another shore that same turn, the unit could not unload. If the unit was loaded into the ship while it was in a city, the ship could sail and the unit could (possibly) unload onto another tile.