Burrows: permanent orders coupled to (larger) spaces (eg. executing jobs there, having access to resources there, "keep this area safe", "keep this area clean",... etc.)
Rooms: functional spaces (eg. private rooms, dormitories, hospitals, workshops, dining rooms, prisons, stockpiles,...)
Designations: issue single, one-time orders to items, possibly more at a time or in a larger space
(and Notes for point-based commands, for the sake of completeness)
You seem to ignore that the very purpose of a burrow is to control where your dwarves go, not what they do. It's tedious to have to make several different farm burrows and then set your legendary farmers to one or a few and set the rest to the rest. Much easier to make two burrows. One for legendaries and one for the rest and define them around the work areas (designations).
I do agree with the three categories, though, even if I completely disagree with the definitions for burrows and designations. The point of burrows, as I keep saying, is to let the player define where they want dwarves to go. If you want to keep the rabble out of the treasury, you make it out of their burrow. This has nothing to do with orders whatsoever. Changing the function of burrows will put this main, highly useful function in jeopardy and I don't see the merit when we can just leave a "burrow" as meaning what it means. Follow me down this post and let's see where we get to, though, as I don't think I've given enough exposition on my stance.
I'd actually like to see all three pulled into one interface, so that you select an area and define it as a room, a burrow, or another designated space. Figuring out all the different ways to select a space at present is just silly. Of course, a room should be able to be designated from any single point to fill the enclosed area, and warn about any missing requirements to function as designated.
YES. YES YES YES. Thank you for bringing this up. When I read this, I searched my posts to see if I already said this as I thought I did! I didn't! I'm obviously a very silly person when I drink a lot of coffee.
This, I think, is (or should be) the ultimate goal with these three systems. We should have an interface like the burrow interface that we can use to set, resize, or move all of these things. Then, depending on what we set (Burrow, work order (AKA designation), room, or zone) we can go in and modify the settings. Rooms should have a building-view (q, I believe) display that lets you see what furniture they use and how much of it is in that area. They should also allow you to assign dwarves for that area to "belong" to and tell you the furniture requests/requirements based on population. Zones and work orders usually would have no settings, except for a Farm work order, or something similar, (or room, if you think it belongs there) which would allow you to q it to set crops, rotations, how often it should be tilled and fertilized, etc, etc. Burrows would still function as they normally do.
Keep in mind I support the spirit of that original idea. Re-sizable farms that the dwarves then till, muddy, plant, water, etc automatically based on labors would be wonderful. I just don't think sticking it in "burrows" would be doing either feature a good turn. Burrows are fine. They perform their task admirably and many other features can benefit from the interface they use. The solution is to make a common interface for these things, then. Not merge things all crazy-style into one gigantoblob where you press a button and suddenly you're deciding if you want to make a farm, a burrow, or a sandwich, all of which are different enough things to add to confusion. A common interface is good, but farms don't need to be an option in the burrow settings. They need to be their own separate entity away from burrows and, I think, rooms.