What is a body shop?

When I was 10 this was an acceptable question, but I never asked. These sorts of unanswered questions generally lead to embarrassment sooner or later, or today.
After the hulabaloo of actually changing the tire (props to Em H for battling the headache and enduring my over-zealousness) the doughnut is flat. The flat doughnut is driven at 10 mph to 7-11 (props again to Em H for flipping off those who honked at us, even if it was dark). The doughnut is filled, and all the others. I don't lose any small tire tube caps; success.
"Let's just drop it at the shop," I say as if I know what I'm doing. Em H follows me, we drop the car in the dark, I call and leave a message.
"Hi, my name is ****Paraproject****, I left my car in your lot. It has the doughnut on, need the tire changed, I'll be by in the morning."
Morning: Cold, snowy, I arrive at the shop. Walk in the door expecting to see Click and Clack from car talk, and I'm not far off. Unfortunately, as I struggle to release my key from its ring, Don informs me (me, awkward and confused enough in the closet sized office) that they don't do tires.
"Oh, where..."
"Discount Tire. Take a right on 8th Street. We're a body shop" He says. (Does this happen often?)
"Yeah, this is my first flat... Do you do windshields?" Yes, that's broken as well.
"No, but I'll tell you who's the best. Precise Glass." He writes the name and number in all caps on a hot pink post-it. I laugh.
"Great, great." It clearly says Don's Auto Body outside, I guess that means something other than, "we fix cars." "Ok," I say as I take the post-it, smile awkwardly, and let out a self-depricating sigh. "I guess I'll be back when I need... something else! Haha!" Inside voice, I remind myself, and hustle back out into the cold to the tire shop, which is different than the windshield shop. I also saw a brake shop. Easy. Now to understand the Grease Monkey...