The difference is the Government is the source of all our money. Our labor, productivity, trust, and taxes is what gives our money value.
There are two kinds of money. One kind is the money the government obtains by taxing or creating it out of thin air and spends into the economy to, among other things, obtain the goods and services it needs to fulfill its mission. We call that "outside money". The other kind of money is money temporarily created by fractional reserve banking. We call that kind, "inside money" or "money created when a bank makes a loan." The latter kind of money is the main determiner of the "money supply", and the former supplies, among other things, the "seed money" for the latter.
I have been posting about outside money. When we produce additional outside money which we move into the private sector by spending it in, we print it. We don't borrow it. That outside money is owed to no one, because it is printed. It is not borrowed. Later our Treasury issues securities in the same amount as the outside money that was previously printed. They auction these securities to Authorized Primary Dealers in the Private sector who in turn sell these securities to private sector buyers using what is called "the secondary market."
When our Central Bank wants to buy or sell Treasury Bonds it does so on the secondary market so that the effect of these transactions will register in private sector reserve accounts rather than in the Government's Treasury reserve accounts. Therefore, when our Central Bank buys bonds it causes an increase in aggregate, private sector reserve accounts; when it sells bonds it drains private sector reserve accounts. This is always "outside money" involved in these transactions. Of course money is fungible and an "inside dollar" can't be distinguished from an "outside dollar" in any way other than by the transaction itself. Any transaction which moves money between the private sector and the government involves, by definition, outside money, and any transaction between private sector parties involves "inside" money.
When the Treasury auctions bonds to private sector, primary dealers it is not borrowing, even though that's what we call it. It is, in reality, just exchanging an interest bearing i.o.u. for outside money previously created and spent into the private sector.*
The aggregate deficit represents the total amount of money we have created to supply our economy with the money it needs for seed money and to function. As long as the economy and population grow we will need to increase the aggregate deficit if we want to maintain a constant purchasing power for our currency. If we create a bigger deficit than that we will experience inflation. If we produce a smaller aggregate deficit than that, we will experience deflation. We will never pay off the deficit but it could shrink rather than grow if the economy starts shrinking.
All of the above is what happens in theory. In practice human psychology plays a major role, especially in the short run. In particular, if our politicians do not correctly understand these basic principles behind sovereign fiat money, they might do very stupid things such as placing an arbitrary limit on deficits or referring to the aggregate deficit as "debt", etc. They might also do these things intentionally if they want to mislead the Public for nefarious purposes. Most people naturally equate government finances with their personal finances, so they are sitting ducks, so to speak, for unscrupulous politicians.
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*Treasury Bonds have a critical role to play as a tool of Central Bank monetary policy and as an interest paying store of money. They serve to temporarily sidetrack money that could otherwise be circulating in the private sector economy. But they do not represent Treasury borrowing!