It's called Safari push notifications because Safari is where the user will first become aware of it. Apple don't name things for developers, they name them for

It's called Safari push notifications because Safari is where the user will first become aware of it. Apple don't name things for developers, they name them for users. Yes it makes no sense to a developer who knows what's going on, but a user will only be confronted by it in safari and that's likely what they'll need to google for if it confuses them. "Why is safari asking me about notifications?"