is cheese cake a cake or a pie?

Neither, it's classed as a tart.

it's a cake.    

I think it's a type of cake hun.

It’s not called cheese pie.

Pie.              

pie is defined as a dessert consisting of a filling (as of fruit or custard) in a pastry shell or topped with pastry or both,   

cake is a bread-like food made from a dough or batter that is usually fried or baked                      

Paradise on a plate