给一般老百姓个人服务的叫“零售银行”或“个人银行”；
commercial/retail banking and private banking are completely different businesses with the lateral one focused more on wealth management. indeed most commercial banks don't offer any private banking services, which aren't prepared for 一般老百姓 anyway.
给“大公司”“大机构”服务的叫“批发银行”或“商业银行”。
it is more common to call this sector corporate banking than either of the two you suggested. 'wholesale banking' is actually a union of pure corporate relationship banking and some elements of investment banking, like corporate finance & capital markets. Not sure what you meant by 商业银行, if it was 'commercial bank' it should be included in the retail banking side and if it was 'merchant bank' the convention dictates it to the private equity alike business, which is a misnomer itself.
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