Algebraic notation records a move using a piece letter and destination square. Nf3 means a knight moves to f3; Bf4 means a bishop moves to f4. Pawns use only the destination, such as d4. A capture includes x, a check includes +, and checkmate uses #. Kingside castling is O-O and queenside castling is O-O-O. The letter N distinguishes a knight from the king, K.
Sometimes two pieces of the same type can reach a square. Nbd2 identifies the knight from the b-file. Pawn captures include their starting file, so exd5 means the e-pawn captures on d5. Read the board as well as the symbols: notation tells you which move happened, but does not explain whether it was a good decision.
Move order describes the sequence used to reach a position. The London setup in the diagram can arise through either an early Bf4 or an early Nf3. When the pieces, pawns, side to move and relevant rights match, the lines have transposed. That lets you reuse knowledge instead of memorising the same position twice.
However, delaying a move can give the opponent an extra option. An early ...c5 or ...Qb6 may require attention before you complete the usual London setup. When comparing two sequences, ask what each player could have done between the moves, not just whether the final diagrams look alike. Practise the branches where the opponent can exploit that difference.
Try this at the board
Replay both London move orders in the caption and check whose turn it is at the final position.