Depends on what you’re talking about, to be honest. The “element” is the “thing”. The “tag” is how you tell the browser what you want.
This is why you have DOM functions like “getElementsByTagName”, which allows you to say “I know the tag name is “hr” (and the tag is <hr />), but I want to get references to all the elements which are defined by that tag.
As a general rule, if you’re thinking about a “thing” on a webpage, you’re think about an element. If you’re thinking about what you need to write to get that element to appear on the webpage, you’re thinking about a tag.
Most of the time, folks will understand what you mean even if you use the wrong one though.