Sky fog gradually moves over time with the clouds. If you are still and watch the fog of the clouds, the fog will move slowly over time. The fog shouldn't be moving at all if the player isn't moving.

A similar thing causing choppy fog movement is caused by when the distance the clouds have travelled is the width of a chunk, still when the player isn't moving. it causes something similar to MC-227139, though that is caused by the player crossing chunk boundaries primarily, since the sky fog jumps sharply when the player crosses a chunk boundary

In the attached video, both the smooth movement over time when the player isn't moving and the jump when it crosses a chunk border are shown, but this isn't the same bug as MC-227139 because that is caused by the PLAYER crossing chunk boundaries. This bug is fundamentally different and is caused by the cloud fog being tied to the movement of the clouds themself, not the movement of the player relative to the chunk.