In The Unadulterated Cat, eleven sub-species of Real Cat are presented for inspection. However, it is made clear that these distinctions are icing on the cake, or rather the entrails on the pillow. It all boils down to one simple apercu:
A Real Cat is what you are, not what is done to you
Real Cats can hear a fridge door opening from two rooms away.
Real Cats have an innate distrust of white coats and can predict the future very accurately when it involves vets. They can erupt from even the stoutest cardboard box like an ICBM. This generally happens in a crowded waiting room.
Real Cats catch things.
Real Cats eat nearly everything of what they catch.
The Schrödinger's Cat experiment was in reality an experiment on Schrödinger by his Real Cat. The intention was to develop a means for cats to travel independently up and down the space-time continuinuinuum as and how it suits them. Sensing a ploy to get him to the vet (well, from the cat's point of view, why else do humans seal a cat into a box?), Schrödinger's Cat took advantage of the escape route offered by all the stray quantum that was slopping around, and nipped around a corner in space-time to a more congenial Somewhen. And once one cat had managed it... (Reference Greebo's trick in a tight corner of Turning Human - a similar learning strategy applies here). The all-white kitten You who cohabited with Granny Weatherwax has taken this a step further: having trained Granny into using her pointy headwear of office as a handy cat-transporter, You was apparently working on the concept of Schrödinger's Hat.
All this and more is discussed in The Unadulterated Cat
Real Cats of the Disc and other Pratchett writings: