I went to Pirelli performance centre to ask about homologated tyres last month.
Mine came from factory with AMS rears and JLS fronts (which is correct for mine - and the correct winter tyres are "J" all round).
The difference in homologation is the compound across the tyre and structure which are generally very slight and quite small and are different due to manufacturers requirements for handling, bias and mainly chamber/toe setup. They seemed quite knowledgeable on the subject and only identified BMW and Porsche as being visually and noticeably different due to chamber angle on BMW and rear weight in Porsche 911's.
I've had two new rears from Pirelli which are the new P-Zero ones of which there are 56 different OE homologations, including some of the worlds most prestigious cars, such as the Lamborghini Centenario, Pagani Huayra BC and McLaren 570S GT.
Car insurance wise, as long as size and speed rating are correct then you should be OK. No car policy I've seen states correct homologation. I stand to be corrected if anyone can find anything. Although why put on a Mercedes tyre on a Jaguar. Although would you notice under normal driving? Although if you car span out of control on a bend would your car insurance check homologation? I would guess not 99.9% would not. Possible grey area. There was a survey on car insurance and tyres and only a very small percent confirmed they knew what the markings on the tyre actually meant!
According to Pirelli
The reason homologation makes sense is this: “The advanced performance and technical characteristics of today’s premium and prestige cars can no longer be sustained by identical tyres for every model. The ingredients of Pirelli’s perfect fit strategy are dedicated technologies, processes and materials. By blending these elements together, in accordance with the needs that each manufacturer’s engineers identify right from the design phase, Pirelli is able to develop tyres that are tailor-made for each car.”
You could argue it would be like hiring a top racehorse out for children’s rides on Brighton beach. In other words, there are horses for courses and a high performance vehicle is going to respond better when shod with the proper boots. Horacio Pagani, founder of Pagani Automobili, expressed it more eloquently as: “People don’t realise the engineering that goes into a tyre. The tyres are the shoes of a car, determining how, when and where a car expresses itself".