There are no set number of moves until players reach stalemate in chess. Stalemate occurs when neither player can check or reach checkmate.
A stalemate traditionally occurs later in the game of chess when there are only a few moves left for both players. It simply means that both players are at a draw.
On the contrary, a checkmate occurs when the other person has secured a win. Their opponent is unable to make any moves to either win or destroy the person's opportunity to win. When someone puts the opponent in "check," this simply means that they can win with their next move.