There are a number of differences between these two currencies:
Bitcoin is a decentralized currency controlled by no one while fiat currencies are controlled by the bank or government.
There are no fees and the transaction time is minimalized when doing Bitcoin transactions unlike with fiat currencies which require these fees so banks can stay active.
A major difference between bitcoin and fiat currencies is the fact that there is no need for authority when trading with bitcoin, rather it relies on the users who will combinedly authorize the transactions.
Unlike the dollar, bitcoin does not have any physical backing. The use of bitcoin has paved the way for more virtual currencies with no physical backing to develop.
Overall, the relationship between Bitcoin and fiat currencies is a very complicated one as bitcoin’s general aim is to challenge the use of traditional currency as a source of payment, yet is purchased most often through fiat currencies.