That would be a 38 Double Action, 4th Model, since there was no S&W Model 4. Is the serial number on the antique side or modern - antique cut off serial number is 382,022? Without the gold medallions, those pearl stocks would be post-factory and originals would have been black hard rubber.
6" 38 DAs are not as common as the other barrel lengths and gives the gun a more potent image, looking like a small hogleg. They do shoot well and are fun to take to the range. Value is low due to the fact that over a half-million were made and most are still in shooting condition.