Both of them check the application from the user's point of view, so, what it's the difference between them?
I think the definitions of black box and end to end testing could vary based on the context of your project. I have seen different people use these terms to describe different things. That being said, usually this is what the 2 terms mean-
Black box testing - This refers to testing the system or the application as a black box where you give different inputs and expect a certain output without necessarily knowing the internals of the system. There are various techniques under this like equivalence class partition, decision table testing etc.
End to end testing - This refers to testing the system based on end to end user flows, instead of testing the system has separate components like in unit testing or story level testing. For example - Logging into the application, then adding a product to the shopping cart, then going to the check out screen and then placing an order and then logging out of the application could be one user flow.