Susans wiki states that:
bigenderBigender (bi+gender) is a tendency to move between masculine and feminine gender-typed behavior depending on context, expressing a distinctly male persona and a distinctly female persona. It is recognized by the APA as a subset of the transgendered group.[1] While an androgynous person retains the same gender-typed behavior across situations, the bigendered person consciously or unconsciously changes their gender-role behavior between primarily masculine and primarily feminine, depending on the situation.
androgyneAn androgyne is a person who does not fit cleanly into the typical masculine and feminine gender roles of their society. Much in the same way as androgyny, androgyne can be used in two related ways: on the one hand, to refer to someone whose gender role or presentation is not typically masculine or feminine, and on the other hand to someone who claims a gender identity outside male and female.
Many androgynes identify as being mentally "between" male and female, or as entirely genderless or the Third Gender. The former may also use the term ambigender or intergender, the latter null gendered, non-gendered or agender. They may experience mental swings between genders, sometimes referred to as being bigender or gender fluid. Some experience severe enough gender dysphoria that they seek HRT or surgery to bring their body more in line with their internal gender, or lack thereof.
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So it can be argued that the bigenders are binary (although i know many that aren't - i see us as kind of genderfluid), and the defining characteristic of bigenders is the gender switching that occurs depending on context (although from reading the above definitions that's true for some androgynes as well). It's that silly label thing again.
I have two genders; my boy mode tends to be an androgyne while girl mode is all girl. The switching is..... rather bizarre when it happens, and i'm not always aware of when a switch is occurring. That puts me into some interesting situations when i switch genders at inopportune times; it's rather weird to suddenly be thinking of painting my nails and what heels would look nice while sitting in a business meeting with a bunch of men

I considered myself an androgyne for a long time before figuring out that i switch genders; i do hope that i my membership card to the unicorn forest still works