Under the sun refers to anything (and everything) which has the sun above it. If you were in the shade, you would still be under the sun, because the sun is above you. The phrase 'everything under the sun' is used to emphasize the word 'everything'. 'In' the sun means that the sun is shining directly on a person or thing. If I am in the shade, I am not in the sun. I would have to walk out of the shade, with the sun shining directly on me, to be in the sun.

The difference between in the sun and under the sun is that, in the sun it is normally in the public eye while under the sun it is normally on earth or in the world. The sun is normally a star that is the basis of the solar system that sustains life on earth and the main source of heat

The difference between in the sun and under the sun is that, in the sun it is normally in the public eye while under the sun it is normally on earth or in the world. The sun is normally a star that is the basis of the solar system that sustains life on earth and the main source of heat