Is the charge nurse the boss of unit secretary?
It's unfortunate these two are experiencing a personality conflict or yes perhaps your friend is being treated unfairly.
Either way, whether or not the Charge Nurse is the boss of the secretary is irrelevant except to say that if you're thinking your friend could sort of tune out this nurse and do her job however she sees fit without the CN's input - - no, not really. CNs and all nurses are expected to use professional judgment that may mean that things will be done slightly differently or prioritized in a different manner than the exact step-by-step function the secretary was taught. In addition the CN is in a role that requires significantly more education related to the contributing matters at hand.
Should she sit there and nitpick your friend? No. I can't say as though I've ever seen that situation without a good hefy dose of inappropriateness coming from the other direction, too, though. Frankly it sounds like the two of them should seek to have a proctored meeting where they can discuss how they got off on the wrong foot.
It won't do your friend well to make this seem worse than it is. For example: Either she's being targeted racially or she isn't. But whether she is or isn't, isn't something that's excused or not excused based on whether the CN is "the boss" or not, KWIM?
I hope your friend isn't looking to take a "you do your job, I'll do mine" attitude because that isn't going to work. If there are real issues, she should seek to address them in a manner appropriate to a workplace. If there aren't, then, if she wants this job, she will have to work under the direction of the CN.