"Now I'm confused"
Welcome to the club!! S&W has one of the most convoluted means of determining model numbers I have ever seen. I'll try to simplify what I wrote later.
The full name of your gun is the "K-38 Combat Masterpiece, M-67". The blued version is the ".38 Combat Masterpiece, M-15" This differs from the ".38 Military & Police, M-10" by having adjustable rear sights and a different style front ramp and an adjustable trigger stop. I don't remember if the stop is accessable from the outside of the gun or not but if it is, it should be found behind the trigger about were it enters the frame. I think it uses an Allen key or maybe a small screwdriver and is actually an internal stop rather than an external. I'm going off recollection and an old poster so my sources aren't very detailed.
The target model of the M-15 was the K-38 Masterpeice, M-14 which came with a 6" or 8 3/8" barrel and the Partridge style front sight of the M-10 for about $10 more in the late 60s/early 70s. It also came in a single action only version which surprisingly was still called the M-14 but Single Action is added to the name.
The M-10 you are familiar with but the alloy version is known as the .38 Military & Police (Airweight), M-12, both came in square and round butt versions.
Your M-67 is a vastly upgraded M-64 (stainless M-10) which added about $20 to the price of the M-64, $35 to a M-10 back when the MSRP for a M-10 was a little over $100.
Popular options that were available include target hammer (rather braod and lower than normal with deep checkering), target trigger which was wide and grooved, and target stocks which were generally a little wider and often had a thumb rest of some sort. Other than police issued guns, I think these options were pretty much standard on privately purchased guns, at least the ones I recall seeing.
In any event, you have a very nice gun, one that should bring many years of enjoyment to you.