One type of diz is used in the final step of combing fibers. It is a piece of wood, metal, or other stiff material with a small hole in it. Spice jar shaker lids work in a pinch. The hole in the diz controls how much fiber can come through at one time -- it gets all bunched up and hard to pull, if you are pulling too much through. So, it does control the thickness of the resulting top.
You can still draft it out finer in spinning, and dizzed top usually drafts very easily, if you want a finer yarn.
I have dizzes with many different hole sizes in them, right down to barely a millimeter in diameter. I'd say I usually use a hole size of about 1/8 of an inch, and get a healthy size of top out of that.
The top does fluff out once it's through the hole, so it's larger than the hole size.
Another type of diz is a "plying diz" -- this typically has 4 holes roughly the same size, though I have a paddle-plying-diz with about 10 holes on it (like I'd ever spin a 10 ply!). This is great to keep your yarn organized when plying. My primary use of a plying diz (and I admit, I will use a combing diz for this if it has 3-4 different hole sizes on it -- whatever's handy) is when I ply cotton. I put my cotton quills from my charkha in their lazy kate, put the ends of the cotton through the plying diz, and push it down near the kate. Then I ply away on my wheel. This helps keep the cotton organized as it's being pulled off the charka quills/spindles. Mainly I 3-ply my charka-spun cotton, though occasionally I'll do a 2-ply. It depends how thick the singles are, since I need a laceweight/fingering weight yarn for my never-ending handspun woven totebag.
(expansion of a post by me on spindlers, this month)