I'm not sure why you got voted down for that - perhaps because you just wrote things as if they were stupid slogans. Since what you write is true (well, except you neglect to mention the difference in maturity and interest rate between US$ and Treasuries), let me elaborate.

Both US$ paper bills and US Treasury Bonds are liabilities of the government (where I consider the Fed as part of the government for obvious reasons). I use liabilities in an accounting sense, but you really need the basics of accounting down solidly to understand the monetary system.

Another term for liabilities is debt. So when you have a 1$ bill, the government "owes" you something. Here's where things get a bit confusing, because what exactly does it mean that the government "owes" you 1$?

Well, they have to extinguish the liability in the agreed-upon way. Usually, you extinguish a liability by moving a corresponding asset that is on the same level or higher up in the pyramid of liabilities (see here: http://neweconomicperspectives.blogspot.com/2011/09/mmp-blog...). When I owe you something, I extinguish my liability to you by giving you paper money.

But the government is at the top of the pyramid, so their liabilities can only ever be transformed into either another form (exchanging cash for bonds or reserves or vice versa) or they can be extinguished when you pay taxes.

That takes some getting used to, but nobody said economics was always intuitive.

thank you!