I am unable to understand why Photo 1 a stalemate and Photo 2 a checkmate.
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Checkmate: When the king is under attack but there is now way to defend it.
Stalemate: When the king is not under attack but none of him or his army can move.
King Can move one square at a time. So just look at one place around the King. With the above definitions.Also, a king can never go on a square that is attacker/controlled by an enemy piece. It Will be clear.
For figure 1. All the neighboring squares of the king are already under attack so king can't go there, only other piece on the board is a pawn which is blocked by the king himself(pawns move forward only unless capturing in which case they move diagonally forward instead of straight forward). Hence, the king or the pawn cannot move hence stalemate.
For figure 2. All neighboring blocks are already under attack plus the king is also under attack hence black has no move to play. So, its a check mate.