They are technically the same in boundary training: using the method of conditioning to make your dog behave a certain way when they hear a signal. The difference is who is giving the signal.
With active training, you’re calling the shots and your dog sees you and hears you, (and smells you. that’s important). Your dog not only learns the commands and boundaries but also learns to follow you and your body language. With simple obedience training, you can tell them to stop when they reach a certain mark, like with flags. Seeing you do the commands also improves their social and mental health and that still works without the use of electronic collars.
With passive training, the device does all the work for you, which is good if you don’t have the time to handle the training or have too many dogs to cycle training from. The devices will still do the same process, they will beep first, then shock if the dog crosses or comes too close to the wire. They will associate the beep with the shock, and therefore stop when they hear the beep. That’s all it does. It completes the goal though, but without all the nice bonus of social, physical, and mental development for both you and your dog.
Both can reduce unwanted behavior like going out of your yard, but with remote shock collars you can promote proper behavior and with the right guidance, even reduce aggressive behavior should your dog have any.