Thats a good question. The earlier New Services, aka the first 21k or so, are known as old models. They have a different trigger guard among a few other differences. Then there were some transitional models that had improvements here and there. The later ones, after 1917, are referred to as "Improved" which is the New Service many of us recognize. Alas, I have only owned one new service, a .455 British contract gun that I sold because it was a little rough. I also had a total custom Colt 1917 that I traded. I'm not big on customized older guns, unless its a King gun or something.
There were also target versions which different from Shooting masters - something I did not know at one time. I had assumed that the NST was replaced by the SM, but not so. They were made concurrently, but the NST was first. The SM was fancier, I think it had better sights, different checkering to the hammer, checkered front and rear strap, checkered trigger, and had different grips. However, you could have probably special ordered a NST with at least the SM hammer and grips, for extra, if you wanted. I would love to find a SM but I might go look for bigfoot instead.
Here is a beautiful "old model" (the gun is also a target model):
Here is a new or "improved" model which most were. 1917 until the end of production, approx 1940.