The difference between a jaguar and a black panther is superficial. They are exactly the same cat except the black panther is a melanistic version (charcoal black version with ghost spots) of the jaguar.
What I have just written is correct provided the person asking the question has in mind an alternative version of the jaguar when referring to a black panther. I say this because the term “black panther” is used generically to describe a melanistic puma (rarely), jaguar or leopard.
So we might be comparing the jaguar to a leopard or a puma. However, in my view the term “black panther” is most often used to refer to a black jaguar. The word “panther” derives from the “panthera” genus a classification of cats which includes the leopard and jaguar (but not the puma).