No the cannellini beans and butter beans are not the same.
The beans cannellini beans and butter beans are similar to each other but they are different.
Butter beans are essentially just the same as Lima beans which they are and the butter beans or Lima beans are also known as Sieva beans.
The cannellini beans are just kidney beans with a different name.
So when you buy butter beans you're buying Lima beans and when you're buying cannellini beans you're just buying Lima beans.
So that is the difference between the two of the types of beans.