[Rivière]

I think it depends on cultural views. It's like in the UK, a biscuit is a sweet treat. Whereas in the US, a biscuit looks more like a British scone and is something that goes with gravy (ew by the way).

I imagine it's down to the intention of its creator, and their cultural background. The cheesecake was created by the Greeks. During its creation, the cheesecake has evolved and changed over thousands of years. In essence, it's called a cheesecake, but is nowhere near the same dessert it originally was. The English adapted the dessert with a different tart base, but kept the name.

Ultimately, I think it's down to culture and opinion.

Personally, a cake to me involves a sponge. A pie involves pastry. The modern cheesecake has neither.