There is a big difference between dog training, dog obedience, and dog behavior. You can have a dog that is well trained but still behaves poorly. Let me explain. To me, dog training is simply teaching certain commands such as sit, down, stay, come, etc to a dog. Most of the time the dog is conditioned to do those commands for a reward, they will comply when the act of listening to you directly benefits them. Dog obedience is when a dog will listen to their handler/owner no matter the scenario, circumstance, distraction level and most importantly whether or not there is a reward in it for the dog.
Dog behavior can by defined by how well or not your dog behaves when they are not in command. What choices do they make on their own? Does your dog jump up on people? Does your dog bark or bite? Does your dog get protective over food/toys/people? Things of that nature. So you can have a dog that will sit, down, stay, come when called, but what happens when you do not give them a command to do? What behaviors do they default to? Do they go crazy when guests enter your home? Or are they conditioned to be calm and well-behaved?
It’s important to have a well-rounded and balanced approach to teaching your dog what you want from them. Show them what behaviors you expect from them, teach them commands that are practical and that you can implement in their lives to make things easier for the both of you. And make sure those things are nonnegotiable, that they need to listen to you no matter what.
I think it’s extremely important that our dogs listen to us whether they want to or not because it always benefits them. Maybe not in the sense they would like (physical food or toy reward), but it’s always in their favor to listen to their handler/owner because it will allow them ultimately more freedom.
Let me give a simple example. You’ve got your dog off-leash, they see a squirrel, cat, or other dog across the street that has their interest. You see a car coming… you recall your dog… at that moment, trust me, I’m sure your dog would rather go chase or investigate what is across the street. It is in their best interest to listen to you, to come back to you, to not cross the street because of what could happen. Dogs need to learn to listen to their owner/handler no matter what. That is dog obedience, when your dog would rather do something else but will still listen to you.
There are lots of different training styles, techniques, methods out there today. It is your job as a dog owner to research the options available to you, and choose a trainer or training style that will help you reach the goals and expectations you have for your dog and that fit your lifestyle.