Lots of great snake pictures
Here are some of a big hognose that was hanging around my house a couple of years ago. First really big one I'd seen here, though usually every year I see young ones, (which is a really good sign, since they're one of the "species at risk")
Hazel, I don't know if you have the same snakes there as I do, but around here snakes with orange/red bellies are either northern redbelly snakes or ringneck snakes. Both are smallish snakes and the redbelly is brown with a creamy spot on each side of it's neck and it can have darker brown stripes running the length of the body, like the picture you posted (not sure if that was what you referred to as a brown garter snake, can't see if that one has a red/orange belly or not). The ringneck snake is slate gray with a creamy ring around it's neck.