Banks do normal Banking Procedures like Parking Your Funds
on safe custody for your use and the pattern you would like
to. For e.g. If you want to park your Funds for your day to
day needs, it can be kept in the Savings/Current Account, in
FD and other fixed Instruments for your Long Term Needs, in
Flexi Accounts jointly for the above purposes etc. 
Mutual Funds are Money managers, who advise & invest your
Money on your behalf in various Funds according to your
needs for a specified period.
A Bank can act as a Mutual Fund Manager but a Mutual Fund
cannot act as your Bankers on all the cases.