First Welcome to the forum !
There's alot of knowledgeable folks here that enjoy helping others by sharing their knowledge, we all got started with one and by asking questions,
S&W's are fun to compare because they have been in business a long time and the only consistent thing is change.
For instance I look at your revolver and immediately see it doesn't have a letter in the serial but doesn't have a flat latch or diamind in the grips so know its after 1967, the large checkering area hints late 1960's , so If I saw it on a table at a gunshow I'd be thinking 1967-1969 ish even if I didn't know the serial number.
If you compare the checkering pattern on your gun to the ones just above on Birdgun's Mod 36 you will see they are the same.
Now compare the smaller checkering area on Cman's Mod 36, his has the smaller checkering area of the ones shipped in the 70's, since we know his shipped in 67 I would assume the grips were swapped.
That's just one small change, if you were to compare Model 36's from every year back to its introduction in around 1951 you'd see alot of changes every few years besides other variations like longer barrels, heavy barrels, front sight styles, grip shape, grip style, finish style, hammer style, number of screws etc etc.
It's all these variations that makes them so much fun to collect and compare but be warned, if you are bitten by the SW bug it's a deep rabbit hole that can become quite costly.
Warm regards from 83F south Florida.