TCisnormativity Project uses di-gender (adjective) to signify the structure of a social-institutional order organized around two principal dialects of gender
Bi-gender (adjective) meanwhile signifies an individual whose articulations of gender varies between feminine and masculine — germane in particular to geographies where a di-gendered social-institutional order is present. A bi-gender person visiting a tri-gender social order may run into confusion from people who are most familiar with that tri-gendered social order.
Example: for a person with a transsexual body — whose dialectal articulation of gender is clearly parsed to pre-existing semantics associated with one of the two social orders in a di-gendered culture — their articulation is either di-gendered feminine or di-gendered masculine (respectively for women and men with transsexual bodies). For quotidian uses, this is shortened to simply feminine or masculine, respectively.
Similarly, cisgender people with cissexual bodies may articulate a di-gendered femininity or masculinity. In these instances, a person comfortable with a di-gendered social-institutional order is probably not invested in the subverting, bending, re-defining, or queering of gender.
Another example: for a transgender person who articulates themselves as bi-gender, they affirm that the dialects of gender they consciously use to communicate themselves to others — namely within in a feminine-masculine context of a di-gendered social-institutional order — may vary as decidedly feminine or masculine.
Both “di-gender” and “bi-gender” speak to systems of communication and social order, as does “tri-gender” in cultural locales where that order is prevalent. Neither are contingent upon morphological or neurological sex.
A note on etymology
This distinction between “di-” and “bi-” is necessary to clarify the subject of gender being addressed. The confusion between a “person who is bi-gender” and “a bi-gender person” produces an epistemological crisis whereby comprehension during a dialogue can be unintentionally lost or misinterpreted.
The Oxford English Dictionary notes how the root for “gender” originates with Anglo-Norman and Middle French usage around the 12th century C.E.
The di- prefix (a variant of “dia-”) is rooted in Greek origins to signify either “twice”, “a-two”, “asunder”, or “apart”. This indirectly informed some Latin uses.
Bi- usage (a variant being “bin-”), originates principally with Latin use and which signifies “having two”, “twice”, “doubly”, or “furnished with two”.
So to use di-gender to signify the “apart” condition of a feminine-masculine social order — and to denote that some people are invested in or have no objections to functioning with one dialect of gender within a di-gender social order — it helps to discern from individuals who do embrace two (or “both”) principal dialects of gender as bi-gender. In other words, the former is descriptive and positional; the latter is prescriptive and self-assertive.