If I go to the bank with a hundred dollar bill, 'deposit' it, whereby my account now shows $100 more, and then go to the bank after a year and withdraw $100 fro

If I go to the bank with a hundred dollar bill, 'deposit' it, whereby my account now shows $100 more, and then go to the bank after a year and withdraw $100 from my account, so that I now end up with a different $100 bill, it's not clear to me how the first $100 bill was state money but the second one was bank money.