Changed URLs, Old one still active

So I’ll try to explain this so I can get some help. I had my website on one URL that I bought from godaddy, but host through fatcow. I recently bought another one to change it over. I went to the wordpress admin section and changed the URL names in the Settings section. Now both URLs work. What do I need to do to only make the new URL have the wordpress on it?

Please explain it to me like I was a 5th grader 😀 I’m unfamiliar with a lot of the server/backend talk. Thanks!