URLs: A specific address for a page on the web that isn't always universal across all users and contexts. Found on the address bar of a browser.
Permalink: An unchanging link that will work in any context and with any user. Found under the permalink option.
In practice, this means that when you're preparing the bibliography of a paper, you'll want to be sure to include the permalinks in the citations, not the urls. When someone clicks on a permalink in a bibliography, there's a 100% chance that they'll be taken to the correct page, but if someone clicks on the url that you've copied and pasted, there's a chance they'll get a "page not available" message.
Basically, if you need to come back to a resource later, be sure to use the permalink, not the URL.
NOTE: In Proquest, the url and permalink are the same thing, so it that particular database you can copy and paste directly from the URL bar.