What exactly IS a "Countergambit"?

I have seen the term "countergambit" and don't really know what it means. I know what it is, but I don't know what makes a move a "countergambit". I know of a few, including the Albin Countergambit, Panteldakis Counttergambit, and my most recently learned one, the Colorado Countergambit. In short, what makes a countergambit a countergambit?

This is a tougher question than it appears. I always thought that a countergambit was simply a gambit played by Black, but I vaguely wondered why no one talks about the Benko Countergambit or the Latvian Countergambit. It seems it more properly refers to a gambit played against a gambit: the Albin is played against the Queen's Gambt, the Falkbeer against the King's Gambit etc. This would suggest that some countergambits could be played by White, but I can't think of any.

Yes, but MOST countergambits take more than 3 moves. (In total by both colors)

Yes, a countergambit is a gambit offered by black.

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There is a 1974 booklet Counter Gambits - T.D. Harding, British Chess Magazine, St. Leonards on Sea, SBN 900846 13 5.
He defines: "any opening sacrifice by black".

Sure, I believe you. Similar to how "defenses" are by black and "attacks" are by white.

It's just strange to me for someone to say "I don't know what it means" ... well, ok I guess I understand. From the title alone it's unclear whether a gambit is being countered, or a gambit is doing the countering.

I always thought it was a gambit offered on response to a gambit. For example when the Queens Gambit is declined by not only not taking the c-pawn but instead offering the e-pawn in the Albin Counter Gambit. The only other example I can think of is 1 e4 e5 2 f4 (King's Gambit) 2 ...d5 - the Falkbeer Counter Gambit. Black declines the gambit pawn offered by White on f4 and offers the pawn on e5 instead.

Yeah, I just assumed it's when your reply to a gambit is to offer a gambit yourself... which may be true in most or all cases, who knows. As long as they make sense, choosing one definition over another is unimportant.

Dictionary says it's a gambit offered by the second player, so it looks like I was wrong.

https://www.merriam-webster.com/dictionary/countergambit

Benko Counter Gambit it is then. Also Englund Counter Gambit. Latvian Counter Gambit.

Looks like a few openings need to be renamed.

Can anyone think of a counter-gambit where this does not apply? I can't.

@11
There are several, all included in the booklet Counter Gambits
Marshall Attack, Two Knights Defence, Benkö Gambit, Hennig-Schara Gambit, Latvian Countergambit, Slav Winawer Countergambit...
No renaming is necessary.
That what we call a rose...

Thanks @tygxc. So there is the "Greco Counter-Gambit" (more commonly called the "Latvian Gambit") which doesn't follow this rule. This is 1 e4 e5 2 Nf3 f5, so Black gambits a pawn and although it was NOT in response to a pawn gambited by White, it is still known as a "counter-gambit". 

Presumably then there are no openings known as "counter-gambits" for White.

Ok. This might sound stupid, but is there a "counter-countergambit"? Or is it just listed as something like, "Paul's Countergambit Declined*, if you see what I'm saying? Btw, "Paul's Countergambit" isn't real; I made it up for the sake of the question.