EV Question - Shareholders

I have always thought that the shareholders were the owners of the business and the bondholders didn't own it, but had a legal claim to certain cash flows. But last semester I took the intro finance class at my university where my professor used the lingo that shareholders only own a claim agains the business- the residual claim. He said similarly, the bondholders own a different claim- a fixed claim on future cash flows. OK, fair enough. But, I am now sorta confused conceptually about bond vs stockholders. If one thinks of the business in terms of the enterprise, then the shareholders don't really own it, they just own a certain part of it, similarly to how the bondholders own a different part.

As you can tell, I am a little confused conceptually about the enterprise value and who actually is the owner of the business. Any help would be appreciated.