There is no inherent contradiction in the use of the terms.
I distinguish between a fine Chardonnay wine and Thunderbird – because I have a discriminating palate.
I discriminate between the writings of Ann Coulter and of Antonin Scalia, because one of them founds his work on a particular legal philosophy and reasons more or less logically from it.
If I were to approve of Scalia’s work and not Coulter’s, not because I consider the import of the writing, but because he is male and she female, then I would be engaging in discrimination just as I did in evaluating the virtues or lack thereof of their prose, but I would be judging on the basis of something not relevant to the work – i.e., their sex. Liking Scalia’s opinions better or worse than Thurgood Marshall’s can be discrimination on the basis of a political viewpoint, a jurisprudential philosophic viewpoint, or because one is white and the other black. The first is questionable ethically, the second sound, and the third reprehensible.
Short hijack: A chairman (chairwoman, chairperson) is a person elected to fill a position where he or she will normally be the presiding officer over a meeting, or given that status as an honor without the expectation of regular actual presiding. The Chair is not precisely synonymous – it refers to the person who is presently serving in that presiding capacity. To make the distinction clear, consider the following: “The Chairman indicated that he had an issue he wanted to bring before the meeting, and named Adam J. as Chair while he took the floor.”
This useful distinction should not be lost in attempting to evolve exclusive language.
BTW, without an intent to provoke an argument on inclusive language, it’s interesting to note that the “-man” suffix in English derives not from the word “man” (i.e., adult male) but from a close cognate with the meaning “human being” that has been subsumed as a standalone morpheme into “man” – compare Greek anthropos and andros, Latin homo and vir, and German Mann and Mensch. So technically, chairman, mailman, bowman, etc., are as referential of a woman holding the position as of an adult male. Note the differing vowels with which they are spoken.