A native application is a stand-alone, non-electron application whose entire stack (runtime, business logic, data engine, and information store) resides on the user’s machine.

‘Hosted’, to me at least, means that you’ve got an augmented web server somewhere on your intranet that you connect to, and that displays its interface through a browser on the user’s machine.

The two terms are mutually exclusive, in my understanding (except of course when one is speaking explicitly of “hosting a web server”, but I’m sure you catch my drift).