I have a current account in Bank Alfalah.
In a savings account you get profit on the balance in your account, but in a current account you will not get any profit.
Current account is mainly for businesses but it can also be opened by individuals. Current account does not have any limit on the number of deposits or withdrawals you make. The charges for banking services vary for current and savings accounts. You should download the SCHEDULE OF CHARGES document from the Bank Alfalah website to get a better idea about service charges associated with savings and current accounts.
As far as minimum balance is concerned, I believe that a savings account has a higher minimum balance limit than a current account.
If you want to stay away from interest then open a current account. Also, Zakat is not deducted from a current account. So if you want to pay Zakat on your own it is good to keep a current account.