Real world currencies are valued solely on the desire to have them; GDP and credit worthiness only play a role because they affect people's perception of how stable or valuable a currency is. There is nothing tangible tying the dollar to the US GDP, if everyone decided the dollar was worthless it would be.
The main thing is that since hundreds of millions of people use the USD and you can use it to buy many goods and services, it's difficult to sway the opinions of a large chunk of the population that use it so any change in value will be slow. Bitcoin on the other hand has a much smaller user base so its volatility is much larger.
No, real world currencies are based on the fact that the issuing government accepts it as payment of debts to that government. The fundamental base of the US dollar is that the taxes you owe the US must be paid in US dollars. The rest of its value extends out transitively from there. But it is not baseless, it is built on the fact that if you do not give the US government the dollars it thinks it deserves, it will come and put you in jail.
If this ceases to be a credible threat, it's actually quite amazing to me how quickly a government's currency can become nothing but so much paper, which argues strongly against the idea that the value is arbitrary.
The main thing is that since hundreds of millions of people use the USD and you can use it to buy many goods and services, it's difficult to sway the opinions of a large chunk of the population that use it so any change in value will be slow. Bitcoin on the other hand has a much smaller user base so its volatility is much larger.