How are the wings of an insect differen from the wings of the bird?

Insect wings are part of their exoskeleton - I've found sources stating they evolved from external gills in very small proto-insects that barely needed the extra surface to leave the ground, and the wings became bigger and more muscular from there.

Bird wings are technically arms, with the same skeletal structure as our arms, or any vertebrate forelimb. They evolved from the arms of theropod dinosaurs. In insects, this would mean wings evolved from one of their pairs of legs, but insect wings have nothing to do with legs.

Their flight methods are very different as well. Birds flap their wings, much like a theropod dinosaur would have moved its arms during hunting or balancing. Insect wings move in rapid swimming motions, often in '8' patterns to create lift with both upstroke and downstroke. The only bird I know of that does this is the hummingbird.