The definition of checkmate is to put the enemy king in check such that he can't escape, block the checking piece, or capture it. Even though the game finishes there, it is assumed that the next move would be the capture of the king. With stalemate, the game ends in a draw if the opponent has no legal moves (with any piece), and the king is not in check. But of course, we can imagine an exception to the rule where the king ventures in enemy territory and is then captured, to end the game. Is there a historical precedent for the existence of this rule, was it always like this? I know that chess has evolved over the years and some alterations have been made for the original Shatranz...
Other interesting historical facts about chess are welcome!
That rule has changed a lot over time and has varied significantly across different regions. From Murray's A History of Chess, we know that in chess' earliest forms, three forms of victory were possible:
Checkmate as we know it today
Capturing all of the enemy pieces, leaving the King alone
Putting the enemy King into stalemate
Over time, we dropped the second win condition, but administering stalemate existed as a win as late as 1600 in Spain (although it was considered a lesser victory). In England, up until the early 19th century, administering stalemate incurred a loss, though later the English and Spanish would adopt the French and Italian rule that stalemate resulted in a draw for both players.
I don't know that the history of stalemate follows any historical battle or event, rather it appears to be an evolution of rules including compromise between players following different rulesets. The history of chess is full of such compromise and standardization, which I've covered in previous answers:
[How has the role of the queen changed over time?] (https://www.reddit.com/r/AskHistorians/comments/57nbm6/in_chess_the_queen_is_a_powerful_figure_and_the/d8tj2wi/)