I would say that all three are the same, but I wonder if there is small differences between them. In the end, what I think is that you are testing user scenarios on all of them.
UI testing: user interface testing. In other words, you have to make sure that all buttons, fields, labels and other elements on the screen work as assumed in a specification.
GUI testing: graphical user interface. You have to make sure that all elements on the screen work as mentioned in a specification and also color, font, element size and other similar stuff match design.
Functional testing: the process of quality assurance of a product that assumes the testing of the functions/functionalities of component or system in general, according to specification requirements.
E2E testing: it needs for identifying system dependencies and ensuring that the right information is passed through multiple components and systems.