The first gun is a Hand Ejector Military & Police, Model of 1905, 4th Change. This gun evolved in to the Victory model, and eventually, the Model 10. It's a fixed sight, K-frame .38 Special. It is the most popular single model handgun in history with an estimated six million of them made. The book indicates only a serial number "range" for all the HE M&P Mod 1905 4th Change guns, 1915-1942.
However, we can get "close" on dates by comparing the serial numbers to factory letters from S&W historian Roy Jinks. As your 334135 is earlier than my 357xxx, and I have a factory letter on mine, I can tell you that my revolver was shipped from S&W in the spring of 1921. I found a factory letter for another revolver with a 290xxx and it was shipped on June 4th, 1918. So it's safe to say that your revolver was shipped between 1918 and 1921.
The second gun's serial number shows as 1966 or 1967, it is a Model 10. The grips are not original to the revolver. I do not know much about stag grips. (okay, I'll admit it... I know absolutely nothing about stag grips)
You can get a factory letter yourself for either or both revolvers by contacting Roy Jinks through Smith & Wesson. It's a $50 charge for this service, but the letter will tell you the date it was shipped and to where it was sent, along with all the features it originally had when that happened. Mr. Jinks also includes an historical recap of the model itself.