Here's how you easily tell the model number on all post 1957 or so S&W revolvers.
Open the cylinder, and look in the crane cut (the little recess at the front of the frame just under the rear of the barrel).
You'll see two sets of numbers stamped there. The first set will match the serial number, the second set of numbers will be the model number.
The model number will be a pair of numbers (if the gun is blued) likely followed by a "-" and another number (the engineering change number), or three numbers (if stainless steel, the model number will begin with a 6), again likely followed by a - & another number.
Smith never made a 690, so that's definitely not it. And, right off the top of my head, I can't for the life of me remember the model numbers for the Airweight Bodyguards.
Sigh, getting old sucks.