It's hard for me to answer this, as I see "well behaved" and "well trained" as the same thing, I think it just varies based on what YOU train for.
I know plenty of dogs who have great manners, but they don't know a single formal command. Their owners haven't made the effort to teach them commands but did teach them to be polite to visitors, stay in their own yard, be calm and have self control, etc. Some people teach their dogs these things without even meaning to, by just living with them and spending time with them. Are they well-behaved or well-trained? Both, based on what their owner wants.
I also know plenty of dogs who know lots of commands, who compete in dog sports, but who have horrendous manners with people and in the house because they're kenneled/outside dogs or crated a lot, or because their owners just LIKE crazy dogs and don't want to effect their drive with teaching manners. Are these dogs well-behaved or well-trained? I feel that they are neither, because manners are an important part of training.
Personally, I want my dogs to be naturally obedient & well-mannered. Fozzie is ideal, to me. He has perfect manners around people and in the house, and he knows many commands & knows when to "turn on". That doesn't mean he's a robot, he just knows very well what I want from him and he knows the difference between playtime and chilltime. He also goofs off constantly, he has his sassy moments. But he is incredibly connected to me... I can just look at him, and he knows what I want him to do. I also feel that he TRULY understands what is "bad", as far as counter-surfing, getting into trash, etc. The time that he diarrheaed in my bath-tub, I feel, is proof of that! ( ; I can't even think of the last time he did anything "bad" and yet I've never yelled at him or corrected him. This is one of the reasons I LOVE clickers and force free training. I never force my dogs to do anything, so all of the behaviors I want are something that I capture or lure and convince them is the best thing in the world to do. It doesn't require me commanding them or cueing them or threatening them. So it seems like they're just naturally "well behaved", when really, I have trained them that acting the way I want them to is rewarding.
Gonzo is well behaved and well trained, but he does have his rare dumpster diving, bad dog moments! I can easily trace those incidents back to either stressful home situations or a lack of physical or mental exercise. I think a lot depends on the dog's intelligence and energy level, too. It's a lot harder for a high energy, high drive breed to contain their exuberance. It takes much more self restraint for Gonzo to not jump up on people he loves or pull on the leash or act out his excess energy than it takes Fozzie, because one is a high strung dog and one is a laid back dog.