If your grips are the same size as the steel grip frame of your gun, they are called "Magnas." Up until about 1968, Magnas had a diamond-shaped area of un-checkering around the screw hole on each stock half, so yours would be called "diamond Magnas." The grips on the gun pictured above are an optional, larger stock called a "Target" stock, and these also had a diamond of uncheckered area around the screw holes, thus "diamond Targets."
Your .44 Special is built on the N frame and has a square butt, so you would want to look for a pair of N frame, checkered Target stocks. These generally didn't need to be fitted to an individual frame like early Magnas did and generally won't have a serial number on them from the gun they may have come from, and they were also a popular item to buy from S&W for customers who wanted to "upgrade" a gun they already have.
Like your gun itself, S&W no longer sells the exact same stocks as they did in the 1950-66 era, the current Target stocks don't look much like what the old ones did. The older stocks are available from individuals and you can find them here in our Marketplace section or the usual sites like fleabay.
There is also an industry making aftermarket grips of all kinds, from individuals to fairly good-sized companies like Hogue.
