"The bird is flying in the sky" or" The bird is flying in the air" kindly explain the difference in detail...
The sky is the blue (or black, or cloudy) vault that comprises the visual limit of the eye. Things that appear to be above you such that that vault appears as their backdrop are said to be "in the sky." The tops of skyscrapers appear to be "in the sky" as do birds and airplanes.
But an airplane taking off or a bird flitting from a low branch to the ground is moving through the air, but is not in the sky. A fly ball in baseball may appear to be sky-high momentarily, but eventually comes to earth. It's all about perspective and point of view.
The two words mean slightly different things. "Air" is the gassy stuff all around us; "sky" is what you see when you look up outside and is more accurately considered a location. The easy distinction is that "sky" contains "air" but air does not contain sky.
Using "the" before each word will heavily imply that they are referring to the same location — namely, the bird is flying and not currently located on the ground.
Here are a few examples of each word:
The sky is blue.
Clouds live in the sky.
Look at the rainbow in the sky.
The air in this room is musky.
I breathe air.
That balloon is filled with air.
The sky is the big blue thing above your head. Air is the substance of which the sky is made. In a similar vein, the ocean is the big salty puddle where the land runs out, but water is the stuff in the ocean.
Birds generally fly in the sky. They do, technically, fly in air, but you don't usually talk about birds that way.