When you borrow from a bank for a credit card, loan or mortgage, to evaluate whether they'll make money from you lenders look at three pieces of information – your application form, any previous dealings they've had with you and crucially, the information on your credit reference files.
Most normal financial transactions and credit relationships you have are listed on these files – yet student loans are not included (with the exception of students who started university before 1998 under the original loans system and defaulted).
So the only way loan, credit card or mortgage providers know if you've got a student loan is if they choose to ask on application forms. They can do this and it happens, but in general it's only for bigger value transactions such as mortgages.