Not much difference.
The main issue I have is that counter current is much more effective. As for the design I showed you; no it does not need to go into the tank. By having a pump move the water into the skimmer, and then have the return hang back over the side of the tank, it would be a hang on skimmer. If you were to have your over flow go directly into the skimmer and then have the return flow into the sump, it could also be external.
Your design might work; however, counter-current airstone skimmers are the easiest (and cheapest) DIY.
The main issue I have is that counter current is much more effective. As for the design I showed you; no it does not need to go into the tank. By having a pump move the water into the skimmer, and then have the return hang back over the side of the tank, it would be a hang on skimmer. If you were to have your over flow go directly into the skimmer and then have the return flow into the sump, it could also be external.
Your design might work; however, counter-current airstone skimmers are the easiest (and cheapest) DIY.