Welcome to the forum, and nice shots, rlk!
AFAIK "Nato" is a style, denoting the strap with the long and short ends like on your watch. They come in all sorts of different makes and qualities. Then there is the "RAF" version without the short end which works like a regular one-piece-strap, just like the American mil-straps. There are also Russian NATO straps with metal eyelets. Actually many NATO straps are made in China.
The sturdier straps after the same NATO pattern (Waterborne, Rhino) are rarely referred to as NATO-straps, however, for some reason. NATO-straps is mostly used as a generic term to denote a thinner quality and a single ring on the short end.
Here is a review of the sturdier strap types:
http://www.tz-uk.com/forum/viewtopic.php?t=3056
Eddie's Bond-NATOs (Bond is the distinctive color pattern, not a shape) fall in between ... they are of a wonderful quality. The only thin (actually medium) NATOs I like to wear. Confusingly, I wear a one-piece RAF strap...
Hope that helps. I am confused now and must rest ... :wink: