Change URL on all pages to new URL (DNS Redirect)

My website exists at example.com but the business I work for has their own URL (sample.net) that they want to use. It is a DNS redirect to a dedicated IP, the database is not moving. So, when someone goes to sample.net, my website will show up in their browser with the URL of sample.net.

However, as soon as the user goes to ANY other page, example.com shows up in the URL box. I’ve tried using Blue Velvet’s replacement link program to get all the links changed from example.com/page to sample.net/page but it’s no use.

Would I look at the General Settings and change the WordPress Address or Site Address? Do I have to go into the .htacess or functions.php? I don’t know which option to choose on the Changing the Site URL page.