I'm not an air plane, but I can fly through the sky. I'm not a river, but I'm full of water. What am I?

Why this works

This riddle plays with the meanings and associations of the words "fly" and "full of water." A cloud can "fly" through the sky as it drifts with the wind, yet it’s not an airplane. Additionally, while a river is a body of flowing water, a cloud is also "full of water" in the form of tiny droplets or ice crystals, which eventually precipitate as rain. The clever contrast between these definitions makes the answer—cloud—perfectly fitting!