There are several kinds of vises that are labelled "toolmaker's vise". There are screwless vises and vises that tighten a screw via a handle on the end; some call these grinding vises. Milling vises look like a Kurt-type vise.
Depending on the size, some vises will be taller than others. Milling vises may be a little taller, although some of the larger screwless vises are pretty tall themselves.
The key differences between the two types, at least in my experience, is that the screwless vises are a bit more rigid and usually more accurate. They certainly clamp more than tightly enough for any work I've ever done. The milling type vises are much faster to use and are more than accurate enough for most of us. They also have higher clamping potential if you are doing heavy cuts.
I have both types for both of my mills. I mostly use the milling type vise, maybe 95% of the time. When I need to do something with what passes for greater precision in my shop, I switch to the screwless vise.
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