"white" monarch means no sockets, non magical, non unique, and non ethereal or in other words a normal plain one, I see "white" monarch offered for trade alot, I call them whites too, its just a refrence to color. When someone gets a crappy drop from hell meph they dont say Man I got nothing but magical items from meph, they normally say Man, Meph dropped nothing but "blues" last run, or they just call it crap.
Concerning "white" monarchs, I typically turn them into 4os monarchs, which are "grey" in color, however once a "white" or normal item has sockets and is "grey" it is refrenced by the # of sockets it possesses.
By the way I use norm socket quests to socket items all the time, ive never received an item back with less than max sockets. If anyone wants to test this theory ive got about 8 "white" monarchs I need to socket if you feel like rushing level 1's to act 5 to prove me wrong id be glad to provide the items and characters