In encountering a draw by [x number of moves], when does the draw actually occur? I played a game of chess recently where we agreed to a rules modification: When one player was reduced to a lone King, a draw could be declared after 16 moves without capture/Pawn move. During this game, the player with material delivered checkmate on move 16. So what happens? Does the checkmate count first, or does the draw?
Typically for the 50 move rule it's 50 ply from both sides without a pawn move or capture so the claim can only be made AFTER 50 moves.  The position on the board always stands so checkmate is checkmate.