Stars are point-sources because they are so far away. All the light coming from them passes through one path, and any atmospheric ripples cause all the light from them to be affected similarly, so we see twinkling. Planets are small from our vantage point, but they are still extended sources, so small disturbances in the atmosphere do not affect all of the light reflected off them in exactly the same way. If you look at them through a telescope, you will see the effects of "seeing" (observational astronomy term for atmospheric steadiness), but naked-eye, they appear pretty stable.
Imagine looking through the water of a swimming pool to a point in the bottom.
As the water moves the single point will move around - like a star
But for a body on the bottom - individual points of the image of the body will move but the average position of the whole body (if it is larger than the size of the waves) will stay in the same place.