The only difference is that we cannot hold bitcoins physically in our wallet and that is the reason people don't have faith in bitcoins and prefer to use fiat money as they can hold it easily and that makes them to trust fiat more over bitcoins.
I dont agree with you, if some people dont trust bitcoin means that they are misunderstanding it as a fraud or something but they have no knowledge about bitcoins. But in reality you can convert bitcoin to fiat currency whenever you want. You can easily shop with bitcoins. In near future as more number of people will know about it and they will invest in bitcoin and will use it as their mode of payment and for receiving cross border payments.
The difference between bitcoin and real money will fade away in coming years. On a positive and hyper view, people may forget to distinguish what is bitcoins and what is fiats... lol