What are key squares and critical squares? What is the best definition of key squares in king and pawn vs king endgame theory? Please provide graphics if possible. Is there a difference between &quot;key squares&quot; and &quot;critical squares,&quot; or are these terms interchangeable?
The terms key squares and critical squares are sometimes used interchangeably in chess literature in king vs king and pawn endgames.

A square is called a key square when the occupation of it by the attacking king will secure a win regardless of which side is to move.

2nd through 4th Ranks
In this example, the key squares for the White pawn are e6, f6, and g6.
[FEN &quot;8/8/8/8/5P2/8/8/8 w - - 0 1&quot;]

A Pawn that Crosses the 5th Rank has More Key Squares
In this example, the pawn on f5 has two sets of key squares: e6, f6, and g6, as well as e7, f7, and g7. If White's king can occupy any of those 6 squares, they can secure the win.
[FEN &quot;8/8/8/5P2/8/8/8/8 w - - 0 1&quot;]

The Rooks Pawn are Exceptions
These positions show a draw regardless of which side has the move.
[FEN &quot;5k1K/8/7P/8/8/8/8/8 w - - 0 1&quot;]


[FEN &quot;7k/8/7K/7P/8/8/8/8 w - - 0 1&quot;]

In the first position, Black can simply shuffle his king between f7 and f8 and White makes no progress. In the second position, the move sequences 1. Kg6 Kg8 2. h6 K8 3. h7 stalemate. The sequence 1... Kg8 `. Kg6 Kh8 3. h6 Kg8 4. h7+ Kh8 with a stalemate, or loss of the pawn.
Related Topics
The Opposition
Rule of the Square
Resources
Wikipedia on key squares
Endgame Simulations (against a computer)
ChessDiary #2 - Monday Endgame Pawn Endgame - Key Squares