Here there is no reference to establish this definition, but there is an appended bibliography, which includes, inter alia, Müller and Lamprecht, 2007.https://en.wikipedia.org/wiki/Key_square wrote: a key square (also known as a critical square) is a square such that if a player's king can occupy it, he can force some gain such as the promotion of a pawn or the capture of an opponent's pawn
But elsewhere Wikipedia, whilst also equating the two terms, defines them differently:
In this instance, they reference Müller and Lamprecht, 2007, which is Secrets of Pawn Endgames, published by Gambit.https://en.wikipedia.org/wiki/King_and_pawn_versus_king_endgame#Key_squares wrote:The first concept that needs to be introduced is that of the key square, also known as a critical square. A key square is a square such that if White's king occupies it, White can force the pawn to promotion, regardless of where the black king is and regardless of which side is to move, and against any defense.
I don't have Müller and Lamprecht, 2007. I do have their earlier, more general work, Müller and Lamprecht, 2001, Fundamental Chess Endgames.
This work defines key squares as follows:
However it does not seem to have a definition of corresponding square. However the term corresponding square does seem to arrive undefined a few pages later:Definition: when the king occupies a key square, this secures the win, no matter where Black's king is.
.The game shows that Black can't defend his pawn if the white king reaches d6. This means that the squares d6, e6 and f6 are critical squares of the g6-pawn (if the white king occupies one of them the pawn is lost). If the pawns are blocked, the three squares directly adjacent to the pawn are critical. For White, the critical squares of the g6-pawn are also key squares, because taking the pawn reaches a winning position.
With Black to move it is different. He can reach the critical squares (d6, e5 and f5) of the g5 pawn using the opposition (fight for three adjacent squares) but this is not sufficient because White's king can defend the key squares of the g6-pawn
So FCE it would appear that occupying a key squares wins, but occupying a critical square might gain a pawn but only wins if it also happens to be a key square.
Reading Müller, Chess Endgame for Kids, there are specific and different definitions for key square and critical square:
If the attacking king can reach a key square of the pawn then the attacker always wins
It then goes on to elucidate that critical squares may or may not also be key squares leading to a win.We define a critical square as one that, if reached by the attacking king, it can force the capture of the enemy pawn.
Checking other endgame books doesn't make things much clearer.
Grivas, Practical Endgame Play - mastering the basics gives definition of critical squares but does not seem to mention key squares. It's definition of critical squares seems to cover the case, however, that Müller uses for key squares.
Dvoretsky's Endgame Manual defines key squares:
.Key Squares are what we call those squares whose occupation by the king assures victory
There does not seem to be mention of critical squares.
van Riemsdijk & Hajenius, Veldjes Tellen, 1994 (Dutch language) defines Kritieke velden:
Thus here "critical square" seems to be the term that Müller uses for key square. Moreover, there does not seem to be a definition of "sleutel velden" or anything else which would seem to correspond with "key squares".Kritieke velden zijn alle velden die, als ze door de koning van de aanvallende partij bezet worden, in een gewonnen stelling resulteren en waarbij het niet uitmaakt wie er aan zet is, noch waar de verdedigende koning zich bevindt
Kere's Practical Chess Endings appears to omit both terms.
Averbakh and Maizelis, Pawn Endings seems to muddy the waters further:
(I have to say that I find that woffle particularly unhelpful!)We are forced to conclude that the game is decided by the white king's occupation of QN7 (or Q7). We shall call squares such as these critical, because when White controls them Black is placed in a critical position. Even more correct is to refer to them as key positions, for White must set up that situation in order to queen his pawn.
Fine's Basic Chess Endings does not appear to mention either term.
Anyone able to clarify matters for me?