I was always under the impression that both series' just interweaved with each other, obviously be last episode of The Clone Wars being just before Episode III, but the rest being spread out amongst and between the Clone Wars' series. There are times in both cartoons where the protagonist is alone. This is times where the others could be doing the adventures in the other cartoon. Even Ahsoka wasn't always around Anakin so still had time to go solo.
So we can assume that similar battles are just different battles on the same planets?