I wife has a 38 with serial# on the bottom starts with C 37xxx can some one give me a little back ground on this. Its in exellent shape and shoots good.
That serial number makes it a 38 Military & Police.
Serial numbers ran from C1 in 1948 to C223998 in 1951.
These became known as model 10's when S&W began assigning model numbers ~1957.
They look similar though. There are subtle differences such as mushroom vs straight head ejector rod, pre 5 screw 4 screw guns, 4 line address, front sight changes, patent dates, etc. As a rule of thumb, any time you see a letter prefix, you know its a post war S&W. I actually don't know of any pre WWII S&Ws with letter prefixes other than the Victory series, which IIRC began right at or right before WWII.
Here is a picture of two early 1915ish M&P 38 targets. Basically this is the same model, but with target sights. Notice how much was unchanged between this one and your post war M&P.