Trained VS taught ?

We rescued our Rottie about nine months ago and found she's about the most stubborn dog we've had. The balance, I'm a pig-headed old kraut myself. We understand each other just fine. My thought. I got some books from the library for dog training. I read less than half. There is no way I'd want a dog commercially "trained" but without the ability to think. My observation. From the part of the book I read, the dog was "trained" to act as a robot without reasonable thought of what they were to do. I think this is cruel. My thought. I understand the robotic commands for trail dogs where money is the subject but I think the word "train" has no place in our pets. I teach her that she's not to leave the property. I tell her she's not to eat the Pit Bull's food. I "teach" her other commands I want her to know but she has to do them willing. Not automatically. If some ****** breaks into my home before I can react I want her to be able to figure out the circumstance by herself without relying on a robotic training. I guess this is a moot subject but the other day I was giving her hell for eating the other dogs food. After a minute or so she bared her teeth to me. How do you correct a dog while laughing. Her thought. "ok I'm bad, get over it". A family pet, not programed for profit has to be able to express it's self. I have to continue to learn to understand.. This rescue girl is a learning gem..
OK. I admit.. I don't know what is involved in commercial training....... Flame away..