DSDs (Disorders / Differences of Sexual Development) are the preferred term, as “intersex” is outdated & misleadingly suggests people are a mix of sexes.
Klinefelters is an exclusively male DSD, & the only characteristic that makes a living being female is development along the pathway to producing large gametes. Female birds aren’t XX but they still developed towards producing eggs.
Errors of transcription & recombination happen, though very rarely: most self-diagnosed “intersex” claimants are nothing of the sort, as you can see the minute you ask which DSD they have.
Similarly, some people are born with a partially or wholly missing lower limb, but humans are still a bipedal mammal & included in the Chinese radical for “human” which is a stick figure with 2 legs.