A decorator told me that a certain large DIY chain has all the branded paints like Dulux custom made by them to a weaker formula to keep their cost down.
Having working in dec coatings trade I can tell you this is nonsense. If you get the same product with the same product code it will be the same. if you buy the retail product from B&Q or bill and bobs paint shop it'll be the same.
The trouble is that retail sectors and trade sectors often want different things. A retail customer wants a paint with high opacity, lots of thickener (in general the diy crowd think the thicker the paint the better quality) and a pleasant product to use/clean/live with. Generally the less coats the better, and DIY customers will live with a slightly poorer resultant finish.
Trade are happier and more able to deal with with a less viscus paint, building thin coats, more thin coats in general is better in terms of durability and finish than one thick coat applied with a butter knife! And lets face it your average deccy is happy to spend a bit of time adding coats. You rarely get away with one coat even of one-coat products.
Now where it gets complicated is that of you rock up at B&Q and buy a gallon of willow green, you will get willow green in the ABC123 retail spec, if you go to a dulux trade centre and buy a tin of dulux trade XYZ123 spec in Willow Green, the product may be of a different consistency, but the colour may be broadly the same. If you get them to mix it up for you it will be different again.
Now thickness can get exciting too, most modern paints are thixotropic, that is to say if you mix them the get thinner and then thicken again as they stand.... This is most apparent with Non-Drip gloss. That is also why if you get a mixed paint it is really watery when coming off the shaker. On cold days/with a cold product, or with stubbon (or old) bases an experienced operator will shake the base, then add the tint, then shake again. An un-tinted base will have limited opacity (coverage) and will likely not cure properly (if an oil base) because the hardener is in the tint.
In emulsion, as the OP posted about a problem that seems to be a little more prevalent now is that bacteria get into the paint and live off/feed on the organic thickener component this leaves you with a milky mess that quite often has a rotten egg smell. Ive noticed this occur with entire batches coming off a delivery truck from the factory (rare) or individual tins. It quite often happens with part used cans. Paint including oil based can be frost damaged, this usually manefests as the hardener dropping to the bottom of the can and forming a sticky sludge you can't easily re incorporate and in the case of oils leaves a product that stays tacky or refuses to oxidise for weeks! Frost can also affect thickeners and usually leaves a paint that looks curdled or like scrambled eggs.
With PBWs manufacturers and Brands will often do many many many formulations with all sorts of different names. With PBW in general, be lead by weight, bit that gives it its whiteness and opacity is heavy. One leading manufacturer when i was involved produced 4 retail PBWs all with the Brandname and a slightly different product name....
Kings One Coat White 2.5L + 5L
Kings PBW Emulsion 2.5L, 5L + 10L
Kings PBW Trade Emulsion 5L, 10L 15L
Kings PBW Super Value Emulsion 3L + 6L (priced at the same price say the trade to give the appearance of it being the same product but an extra fill can)
This can catch out in experienced buyers and staff.