Islamic banks collect funds either on qard basis or on Mudarabah basis.
Offering returns/profits only on Mudarabah based accounts as return on Qard is Riba(Interest), which is strictly forbidden in Islam.
Conventional banks identify currency/money as commodity, thus they can trade or rent it and make profit of it.
Islamic economics is based on Islamic law and principles, while conventional economics is based on capitalist or secular economic systems.
Islamic economics aims to fight against practices such as usury, maysir, and gharar, which are prevalent in conventional economic systems .
An Islamic mortgage differs from a conventional mortgage because under Shariah Law it is forbidden to charge interest on a loan, so in this case banks will buy the property on your behalf and rent or lease it back to you for a profit.