I have a brother named Adam. If, after several years of AI being known as artificial intelligence, he got into chatgpt or stable diffusion and started calling his use of those Adam Intelligence and tried to convince the world that is what AI really stood for I would tell him to stop being an idiot and he is making me look bad. He looks an awful lot like me.
I don't currently use Apple stuff, used to use one of their phones and it was decent, but if I was a big Apple fan the term "Apple Intelligence" would be an embarrassment that would drag in the i prefix.
Edit: Apple Intelligence also looks more intrusive than Windows Recall, but less honest. It is AI analyzing your content in basic apps in real time and can you really turn it off? Also an unintended nsfw genmoji would be awkward.