Difference is regulation, real money is regulated by governments or central banks, they dictate the value of real money, while Bitcoin is free as far as I know of regulations from governments, value is drive by supply and demand.
There may be some factors, but the FIAT is driven by the supply and demand too. When the FIAT currency is in demand and that country is not printing more, then the economy is high and the fat will grow. It won't be in value if no one uses it anymore, the only difference is that BTC is purely has a stand-alone law, which is its value purely relies on the usage, unlike fiat that there are so many sectors that is involved and considered.
The differences of bitcoin and $ actually is a lot, but some of them are :
1. Bitcoin characteristic is independent directly from any government
2. The transaction of bitcoin is very transparent just like a cash book of a bank that so far just accessed by the accountant of that bank, but bitcoin
with blockchain technology is allowed to be accessed by anybody.....so the transparency is very high.
3. Bitcoin is allowed to be transacted by peer-to-peer, not via a bank which can shorten the procedure and bureaucracy, and of course the cost.
The transparency is very low when you don't know the addresses of people, that's why it is highly used in trading illegal goods, but when its applications will be used in government transactions and employees know the addresses, then it is much more transparent than any existing fiat.