The main difference is that banks are controlled by government while whales are private individuals like you and me. In some countries, banks deposits are insured as well till certain amount.
Banks and whales are not comparable at all. Banks give loans, take deposits. Whales buy/sell asets on a large scale and use that to manipulate the market. One does it for their and public's benefit while the other only wants to profit from the market movements. Whales are also loan sharks but that number is limited and they are usually predatory in nature.
Besides banks have a lot more number of services to provide, whales are not intended for that.