Yes it is a 32 S&W.
Ballistic wise it would be a bear killer. 
JK 
Actually it's a like a 32 special compared to the 32 H&R mag.
Hello Old fart
To start out with here, I am not
Knocking your gun or caliber, but I will share some Information with you that you may like to know if you don't all ready. The .32 S&W is a very Old caliber that was originally made in Black Powder. They are Not what I would call anything close to a .32 H&R Magnum or even close to the Newer round of .32 S&W Long which is almost Twice the pressure of the .32 S&W round. What the .32 S&W really is
a great target round that shines on Paper. It has a velocity of 650-700 FPS on average where the .32 S&W Long Cartridge averages 800-875 in Factory Loaded form.
The .32 S&W round can be a challenge to find in Factory Loaded form. I know Remington still makes it occasionally, so if you need loaded factory ammo keep an eye peeled for the Remington brand out there. They only offer it in a 98 Grain round nose lead bullet load. I have this caliber in a single shot S&W Target Pistol that was made in 1904 and Hand Load for it as factory ammo is hard to find and in Excess of $30.00 a Box when you do find it.
Your gun was Originally called
"The Terrier". It was the original small frame S&W revolver offered in Pre-War form and early Post-War form. Carl Hellstrom ordered the S&W engineers to design and build a caliber more potent for Police in a side arm Pocket carry revolver, Hence the Model 36 was born in early 1950 time span in .38 Special caliber and fondly called the Chief Special. This design was prompted by Colt Offering their "Dick Special" in the More Potent .38 Special caliber. It differed from your gun as it had a Five shot cylinder opposed to your Six shot cylinder, and of course was in .38 Special.
Sadly, The .32 Caliber handguns lost a lot of Ground once S&W tooled up and started making the Pre-36's in .38 Special caliber. I am Very fond of any .32 Caliber S&W made as they are so Deadly accurate and Just Plain Fun to Shoot. S&W also Offered the Pre-30's then in 1957 they stamped the guns model numbers on them as the Model 30's that look exact to yours but are chambered in the slightly more potent .32 S&W Long Caliber. I have Two of these Pre-30's with 3" Barrels in both finishes being Blued and Nickel as shown. I hope this helps, Hammerdown
