"Extensions" are things like AdBlock Plus and NoScript. "Plug-ins" are things like Flash. "add-ons" is a term that covers both extensions and plug-ins. That's why the add-ons manager has tabs for both "extensions" and "plug-ins".
To confuse the issue, people very frequently use "add-on" when they really mean "extension".
If you go to the Firefox add-ons in about:addons and do a search for an addon called "flash" then a link to the [Adobe] flash plugin isn't presented (as either best match nor name match). It's got to be amongst the top 10 addons used surely?? Certainly one of the top 10 for the keyword "flash". So?
Equally the https://addons.mozilla.org/en-US/firefox/ page doesn't mention plugins at all, not even under the "more" top menu. If you search at the addons page you only get extensions and no plugins offered to you (eg https://addons.mozilla.org/en-US/firefox/search/?q=flash).
Extensions are found at addresses like https://addons.mozilla.org/en-US/firefox/addon/$extensionNam...; shouldn't that be /en-US/firefox/extension/... ?
In short Mozilla don't make it clear to users so how should a user be expected to see the difference? Is there a real difference or is it just an arbitrary Firefox UI distinction?