In fact, when households choose to save more money in bank accounts, those deposits come simply at the expense of deposits that would have otherwise gone to companies in payment for goods and services.

This is an extremely macro view. "All the money is in the system and can be assumed to be in the bank; the account doesn't matter; the bank is the institution through which all money flows, so regardless of where the money is, the money is in the bank."

This article explains how, rather than banks lending out deposits that are placed with them, the act of lending creates deposits

Commercial banks create money, in the form of bank deposits, by making new loans. When a bank makes a loan, for example to someone taking out a mortgage to buy a house, it does not typically do so by giving them thousands of pounds worth of banknotes. Instead, it credits their bank account with a bank deposit of the size of the mortgage. At that moment, new money is created. For this reason, some economists have referred to bank deposits as ‘fountain pen money’, created at the stroke of bankers’ pens when they approve loans.

I think this is silly.

At the end of the day, the bank has a balance sheet. The sheet must be balanced. If banks simply created loan after loan after loan without deposits and other income (fees) they would show marginal income on year-end reports based solely off of the interest made on the loans, assuming all borrowers repay. Deposits are necessary.

I think this article may be making the point that because banks act on such a macro level, they can afford to lend out more money on say, Tuesday, than they actually have in deposits - because they can count on the fact that by Friday, everyone gets paid by direct deposit, it'll even out.

A bank could not fountain pen money into existence if it did not have deposits. A bank can only seemingly "fountain pen" money into existence because these days they are so huge. If I am a small bank or a credit union and I really only have $10,000 of money - let's say some is start-up capital or whatever, but most is deposits - if that is all I have on my balance sheet, sure I can "lend out" $12,000 by simply fiddling numbers in the system, but then I am factually $2k in the hole, and either I have to make that money up somehow or I'm going to be in the red when I report my earnings for the year. I'm not ENRON and we'll assume I'm not ENRON-izing my report.

Sure, at the end of the day, I can lend way more money than I have - if I am a major bank with systems, ATMs, networks, and all the systems that would enable it to appear that that money is actually there. But that money has to come back to me. I can't count on a 100% rate of return on my loans so the interest on the good loans isn't going to be enough to turn a profit, plus not to mention all the people I have to pay in order to service these loans and run my Collections department. It'd be unwise to depend on investments to return that money because basically that's not reliable.

If we have a closed system and there is $100 in the system and Alice has $50 and Bob has $50, sure, Carol can go to the Bank of Ted and ask for $100. The Bank of Ted can even say "Sure! Here, have $100!" but unless Alice and Bob actually believe the Bank of Ted has $100 already, Carol doesn't have $100. Alice and Bob will not believe that the Bank of Ted has money simply because BoT says it has money; it needs to be an accepted fact that BoT is "the place where all the money is." If Alice and Bob know BoT has no money they will not accept BoT's notes.

I feel like I'm missing some sort of point here or something.

Yeah, rereading it, and just not getting it. They're basically saying that because banks use systems and not real money, banks can fudge the numbers and just make it look like there's money somewhere even when nothing happened to make that money appear wrt "real money" or physical money.