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 preparing the bibliography for a paper, you should 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.
Essentially, if you need to revisit a resource later, be sure to use the permalink, not the URL.
Note: In Proquest, the URL and permalink are the same thing, so in that particular database, you can copy and paste directly from the URL bar.