On behalf of all those who hate computer terminology thank you for your question!
URL (uniform resource locator) a technical name for a website address (see p. 387 in “Is This Thing On?”). In other words every website address is an URL.
A browser (such as Internet Explorer, Mozilla Firefox, or Safari) allows your computer to communicate with the World Wide Web (see p. 172-173 and p. 382).
To translate…Internet Explorer (in your case – your browser) allows you to visit my website (URL=www.abbyandme.com).
Does that help? A rose by any other name…If you're connecting to the Internet and visiting websites, you're using your browser and visiting URLs perfectly well without needing to know the terms.
Keep in touch,