Shooting a rifle, there's a very obvious difference between cheap bullets and the better quality. Cheaper are noticeably less accurate. It comes from variation in powder loads and variation in uniformity of the lead. I would expect the same to apply to shotgun cartridges. Inconsistent powder loads and irregular shaped pellets will affect the flight of the lead. So I would expect cheap cartridges to give a variation in pattern.
That said, I miss because I'm not pointing in the right place
However there are very few lead shot manufactures and the manufacturing process is such that all shot is made either by tower dropping or the Bliemeister short drop method. Both process remove irregular shaped shot not to sell on to the cartridge manufacture but to be melted again, put back into the process again.
As for variation in powder load, modern machines are very accurate and very fast, a carton of 25 every few seconds, the same machine will make budget and competition cartridges.
Competition cartridges normally have harder shot, or copper or nickel washed shot.
What makes a cartridge is the bringing together of the powder type (and there are lots, single or double based) , wad type (lots again) and shot type to deliver the expectations of the shooter.
I have been selling shotgun components for home loading for eighteen plus years buying from the same manufactures as the commercial cartridge manufactures do.
The components have been around for decades, yes powder has improved but really the rate of change has been slow, if it ain’t broken don’t fix it.
However not so now with the race for biodegradable wads to use with non toxic shot, like steel shot and the risk of a total ban on lead in ammunition.
A shotgun is a scatter gun, no two patterns will ever be the same