The most prominent difference that I know of is that the Morrowind guild was more structured than its Cyrodiilic counterpart. They tended to give real jobs more often, and kept the freelancing to the side. The Cyrodiilic Guild was more freeform - you've got your duties, your bosses, but freelancing was the heart of the guild economy, and went to greater lengths to set up a fencing system.
I do not know much about Daggerfall's thieves guild, but I'm assuming they also have their primary goals and suchlike.
Spoiler
The Grey Fox is whoever is under the cowl. If I'm not mistaken, when Milord Umbranox used the Elder Scroll to break the curse part of it, it no longer erases the wearer from history, but the disguise part of it works as normal. so in all technicality, the mask could have made its way anyway just like any other artifact. I do not support a guild of cutthroats getting it, though.