if you really need someone to give you a breakdown + application of the idea of fungibility to bribes to see the distinction, here you go:
when you bribe a teacher for a better grade, you aren't utilizing a relationship to induce a change in outcome, you are utilizing money, money that holds value independent of who is providing the bribe.
edit:i am making the assumption that parent read at least the wiki blurb of what the parent is replying to.
Money helps you get to know people, particularly in China for things like getting grades and jobs. If, after you give them money, they then "know" you, money was still part of the equation.