Yep the 7.62x39 is a .308 bore on the TC's. What's great is that that gives you a ton of handloading options. I wouldn't shoot ANY factory ammo through it, the pressures will be high, perhaps not dangerous, but it does increase the chamber pressures. That causes extra stress on the frame. Besides you'd probably be disappointed with factory ammo or mil-surp stuff anyway. It's pretty much a hand loader's cartridge. Bear in mind that reloadable brass is a little hard to come by lately. I try to grab some every chance I get.
I've had a lot of fun with my Bullberry 7.62x39, it's an excellent pistol cartridge, giving you 30-30 performance in a smaller cartridge. I would recommend using almost any handload that is safe for a 30 Herret, the 7.62x39 has a bit larger powder capacity. One of my favorite loads for it is a 180 grain RCBS cast lead spire point with 3.8 grains of Red Dot. Makes a good "plinking round" and is extremely accurate!