The mechanics are literally identical.
We create a wing - air moves over the wing and it generates lift, there's zero difference between an A380 moving through the air and an Albertross gliding, no difference at all.
(of course, the bird generates forward momentum by flapping it's wings, we use an engine or propeller - the rest is exactly the same)
People long ago realised this and tried to emulate nature and flight by creating wings they could wear, they didn't quite succeed at first - but they had the right idea, and it ultimately led to where we are now.