Hi there, Lauren!
An external link is one typeof hyperlink—specifically, a hyperlink that links from one domain to another. The opposite is an internal link, which links from one page on a domain to another page on that same domain. A link from moz.com to inbound.org is an external link because moz.com and inbound.org are different domains, but a link from moz.com/community/q to moz.com/community/q/what-is-the-difference-between-anchor-text-and-external-links is internal because they're both on the domain moz.com.
Anchor text is a component of all text links, whether they're internal or external. In a traditional hyperlink that appears on the page as a bit of underlined blue text, the anchor text is that blue text itself.
This is an internal link to moz.com/community/q. The destination URL is moz.com/community/q, and the anchor text is "This is an internal link to moz.com/community/q." It's internal because both the page we're currently on and the page the link points to are on the domain moz.com. Here's another link to moz.com/community/q: The Moz Q&A Forum. It has the same destination URL as the previous link, but the anchor text—"The Moz Q&A Forum"—is different.
Does that clear things up at all?