This is most likely a S&W 38/44 Heavy Duty. It was introduced in 1930, redesignated as the Model 20 in 1957, and discontinued in 1966.
It was introduced to give LEO’s of the time something better than a regular .38 Special to penetrate vehicles and body armor. It used a souped up .38 Special cartridge initially designated as “38/44 S&W Special”, and later as “.38 S&W Special Hi-Speed” or “.38 S&W Special-X”. Regular .38 Special rounds can be used in it.
Essentially, it was the forerunner of the .357 Magnum.
It was built on the .44 Special frame, not .44 Magnum (which didn’t exist at the time). It was available in both blue and nickel finishes with wood grips. Most commonly it had a 5-inch barrel. It had fixed sights. (There was an adjustable sight version called the 38/44 Outdoorsman, but I think it was only made with a 6 ½ inch barrel.)
It is somewhat uncommon pistol to see nowadays (esp. compared to S&W K-frames), but it is certainly not rare.
It is definitely a well made handgun with an interesting history behind it.