You can use Dollars to do buy zillions of things large and small.
You can use BTC for nothing.
Dollars are backed by assets, not that it matters that much.
So TBills are in fact a kind of 'faith in the governments ability to pay' - but that is a measurable, tangible, verifiable thing.
Euros are generally backed by real estate and other 'high quality' assets.
Most good national currencies are managed that way.
So - the central banks basically control how 'one asset (i.e. real estate) is turned int currency' back and forth, keeping enough currency going so as to allow for economic expansion, and to keep inflation at about 2% and unemployment in check.
At least in theory.