Trying to write out all of the differences between game and store bats could take forever, but I'll try to give it short summary.
Early H&B game bats, would have a 125 in the center logo and a blank, hand turned knob. Store model bats, if a model 125, will have the length stamped into the knob.. 34" 35" etc. Store models will normally be marked as a 40 followed by the players initials 40BR (Ruth) 40LG (gehrig)
Later H&B pro model bats started to get model numbers marked on the knob, which would eventually be moved to the barrel in 70's. Model numbers consist of a letter and number.. c12, r43, g69, 016 etc
Store model bats started to look a little different in the 40's and 50's when the bat markings were painted on instead of burned into the wood. Game bats, pre 1980, the markings will always be burned into the wood, except on adirondack bats.
Please keep in mind, this is just a short explanation and there are many other factors to determine a true game bat. If you post some pictures, we can help you out.
Matt
Bub13@aol.com