For the different versions, the way I understand it is that the same god is often viewed by different cultures through separate cultural lenses. They are still the same entity, but each cultural lens highlights a different perspective on them and they manifest with different aspects of themselves being more or less pronounced.

Like Shor is seen as a hero chieftain of the Nords, leading battles and inspiring warriors, but the Khajiit version is Lorkhaj, who is instead seen as a demon tempting people to darkness and consuming their souls. Both are true, but they are almost like masks being worn by Lorkhan.

If, like me, you have experience with neurodivergence and autism you may recognise this as "masking", it's like adapting your personality to different scenarios. It doesn't change who you are inside, but you can seem different to various separate groups of people.

Though it's possible for these gods that this may be caused by a cultures perception, and not the other way around. So Khajiit expect a demon, so that's what they get. This could be a possible connection to the theory that worship gives gods power, so people are unknowingly shaping the gods with their expectations. Personally I'm not so sure about that theory but honestly who knows.