Bank is Institution that deals in money and its substitutes and provides other financial services. Banks accept deposits and make loans and derive a profit from the difference in the interest paid to lenders (depositors) and charged to borrowers, respectively. They also profit from fees charged for services. The three major classes of banks are commercial banks, investment banks, and central banks. Banking depends entirely on public confidence in the system's soundness; no bank could pay all its depositors should they simultaneously demand cash, as may happen in a panic. (http://www.merriam-webster.com/dictionary/bank).

A bank is a financial institution and a financial intermediary that accepts deposits and channels those deposits into lending activities, either directly by loaning or indirectly through capital markets. A bank is the connection between customers that have capital deficits and customers with capital surpluses. (http://en.wikipedia.org/wiki/Bank)

Based on that definition, both Islamic and conventional banking are the same aim (profitable). Note: World bank is bank (profitable).

There were non-profitable institutions like a bank but not a bank, namely: Baytul Mal (government institution) and Awqaf (Government and society institutions).

Unfortunately, today we can not find baytul mal, because that institution is part of Daulah Khilafah structure.

Wallahu a'lam bishawab

Islamicbanking can be based on profit oreanted. However profit oreantation must be based on objectves of the shariah which is based on preserving the public interest and preventing harm·

Definitely, Islamic Banks are privately owned by investors who looking for profits in the first place. In my opinion, this is the sole purpose of these financial institutions. ,

Should the Islamic Banks aim to be profit oriented?

Before we discuss further, we have to look at the framework of Islamic banking. Are they different from other companies. Basically there are two fund providers namely shareholders and depositors. Similar to other companies establishment the objective of shareholders are to maximize their wealth. As for depositors, they want to keep their money safely at the same time they are hoping for some return in the form of profit or hibah, depending on their contracts with the bank. 

https://www.researchgate.net/publication/305815587_The_Dhaka_Mercantile_Co-operative_Bank_Limited_A_Case_of_Islamic_Shari%27ah_Banking_in_Bangladesh

Article The Dhaka Mercantile Co-operative Bank Limited: A Case of Is...