It's usually the cushion wad & especially a heavy, lubed one, being pushed into the shot charge as it clears the muzzle, that spreads the pattern into donuts.
That is why guys separate the shot from the powder by using 2 or 3 thin overshot cards, not a fiber wad.
In this shadow-graph, you can see the difference between the choked barrel (lower) and the cylinder bore (upper) patterns.
The wad is being pushed into the shot cloud, which has already started to spread out. The bottom picture shows a concentration of shot
in the middle of the shot cloud. These pictures were taken 18" from the muzzles.