To define an Islamic bank, it is preferable to clarify the two key words which are Islam and bank. Regarding the definition of Islam, please refer back to question 1.
A bank is a financial institution or intermediary which accepts deposits, provides loans and banking services, e.g cheque, cards etc.
An Islamic bank is a financial institution or intermediary which accepts deposits, provides loans and banking services according to Islamic principles.
How does an Islamic bank (IB) differ from a mainstream bank (MB)?
An Islamic bank differs from a mainstream bank in many ways. The first and the biggest difference is the intention or the why. An Islamic bank should strives to implement primarily the rules ofl of Allah (SWT) while the first driving force of a mainstream bank is to make profit. If the first difference is well understood, all the other differences are based on it.
Second, an IB must care about the general welfare of humanity, whether here or hereafter, so it does not finance, and ideally, not collaborate with people or entities who might destroy human beings or its natural habitat. For that reason, an IB is not allowed to fund alcohol industry, gambling, entertainment, pornography, tobacco, mainstream financial institutions and sometimes weapenary. On the contrary, a mainstream bank might finance one or all of those industries.
Third, an Islamic bank has the obligation to wait for a genuine distressed customer until they can afford to pay back without any late payment fee while a mainstream bank will highly likely charge a fee increasing a burden of the debt which might make someone question the rational behind these institutions.
Last, an Islamic bank has a social responsibility to provide for the society it operates in by paying zakat.
These are few main distinctions between an Islamic bank and a mainstream bank, although they can very in many aspects such as governance, relationship with the central bank and other financial institutions, capital structure, financial reporting, social responsibility.