My French isn't as great as it should be but I'll take a stab.
vin de égouttage is wine made from free run juice. The word means something like dripping or draining. You leave the skins and seeds and just draw the juice off.
ecoulage is the draining from the tanks after fermentation.
soutirage has more to do with racking than with draining the must of the solids.
But I will totally defer to a native French speaker!