Cross selling means selling of products/services to an already existing customer. And then if we talk about banks, when they sell any extra banking products/services to their customer along with the product the customer wants. Example: selling a credit card and internet banking to a savings or current account customer, selling their any bancassurance products, etc.
Banks have been using cross sell as a marketing approach to expand their footprint and also increase their customer base.
Cross selling also have advantages like it reduces servicing, marketing and communication costs and thereby substantially increases spread for banks also.
Both terms are used interchangeably, both offer distinct benefits. Unlike cross selling, up selling means encouraging customers to purchase a higher-end product or we can say a more costly product than the customer has asked for. Example: the customer asks for a credit card with overdraft facility of Rs 10,000 but the banking representative tells him benefits of having the card with more facilities, etc.