Banks are in the business of savings and loans while Mutual Funds are for investments. When you put your money in a savings account or in a fixed deposit, you are making savings whereas when you put your money in Mutual Funds, you are making investments. Banking and Mutual Funds are two completely different businesses, requiring specific domain and organizational expertise. Banks are governed by RBI while Mutual Funds are regulated by SEBI. If some corporate wants to be in the business of banking and Mutual Funds, it must seek separate license permits from the respective regulators and run these two businesses as different companies.
You may come across some banks that also have a Mutual Fund business. But both are two different companies with no functional linkages and does not guarantee returns just because the bank has a sound track record.
Most banks today function as distributor of many financial products including Mutual Funds. They operate as a sales channel for the Mutual Funds that have tied up with them (banks) for distribution. Hence, if you are wondering how to invest in Mutual Funds and want to approach a bank, remember that the bank may not be selling all the funds available in the market.