The wire size is NOT diameter, it is cross sectional area of the copper itself. So when you have more strands to achieve the same cross sectional area, you have more air gaps between strands and thus more diameter.
Separate issue, because based on your question, it appears you may not know this:
There are what are called "classes" of stranding, having to do with the number of strands in a given cross sectional area. Most building wire stranding is Class B (37 strands) or Class C (61 strands). Mechanical lugs are rated for a very specific maximum stranding class, usually B, sometimes C, so you have to read the stranding class for a lug if using anything other than class B ( which is what your standard THHN cable will be). If you are using something like DLO cable with Class H stranding, (467 strands) you cannot use standard mechanical lugs at all. There are a few mechanical lugs out there rated for Class H stranding, but they are often not off the shelf. The usual way to terminate high strand cables is to use compression lugs, but even then it takes special lugs and dies.
