A large proportion of the mince pies eaten in the UK at Christmas come from the Mr Kipling factory in Hampshire. In fact, they have probably already started making them, as they get shipped to enormous cold stores around the country to await the Christmas season. About October, usually…
However, although Mr Kipling makes mince pies for a number of brands, in-store own brands and so on, they are actually made to different recipes. Economy of scale in that the "making" equipment is well-used that way, but that doesn't mean that you can't use a bit more or a bit less of various ingredients, or add/remove some of them according to taste/preference/price point. Taking a look at the stacks waiting for loading and distribution and seeing various brand labels doesn't mean that they are the same inside.
I have bought an unbranded component for an Audi (rear screen wiper motor) which claimed to come from the same factory as the originals. Although it arrived in a non-Audi box, it was pretty much identical to the original (barring a small improvement or two which was also true of the current Audi replacement) – but about 70% the price.
Problem is – how do you tell? Same factory could mean different product, or same product/different brand, or possibly something altogether inferior. Tricky one!