Welcome to the Forum. The specific model is 38 Double Action, Third Model. They were manufactured from 1884 to 1895, with around 204,000 made. Serial number 205XXX would have shipped in maybe 1888 or 1889. You might wonder why your serial number is higher than the number of this model made? To clarify, the serial number range started with "1" for the 38 Safety, 1st Model and the 3rd Model range was 119,001 to 322,700.
The comment on a refinish is supported by the fact that the hammer, trigger, and trigger guard were typically not nickel plated. Overall, the plating looks very well done, with even the pin holding the front sight not buffed flat. Also, looking at the hard rubber stocks, they look well worn, which does not match the current level of finish on the gun. Still a very nice and priceless family heirloom.