Answer:
They evolved from entirely different ancestors, but both developed wings in response to similar ecological conditions.
Explanation:
Based on the info given, they possibly could have had the same ancestor, but even if that was true, the bat would have some type of resemblance other than wings. I think that due to environmental changes, natural selection allowed these organisms to fly so they can survive in that environment. Birds got feathers because they could have been in a cold ecosystem so they needed warmth for themselves and their young as well as stay away from predators, due to their small size they had no way to get away without wings. They didn't have legs for running so they developed wings. Bats may have been in a fine temperature, but the day caused problems due to hunting, so they developed wings to hunt at night and keep themselves in caves to hide from predators.
This is the best I could do, I hope this helped :)
