Various scholars have proposed terminologies for a taxonomy of diglossias. For what here is referred to as `classical' (Ferguson 1959) and `extended' (Fishman 1967) diglossia, Kloss has proposed the terms `in-diglossia' (for the kind where the two varieties are closely related) and `out-diglossia' (for situations where the two languages are unrelated or at best distantly related) (Kloss, 1966: 138.) A classicist might prefer something like `endo-diglossia' and `exo-diglossia', i.e. prefixes that fit better with the original Greek roots of the terms. But it is clear to some researchers that there are important differences in the dynamics of societies characterized by the (at least) two basic kinds of diglossia. Fishman has also proposed a useful distinction between `consensually different languages' and `consensual dialects', since there is an unresolved debate as to whether Caribbean English (for example, but any Creole language/dialect could be used) is in fact genetically descended from English, i.e. is consensually a dialect of English, or is consensually (agreed to be classified as) a separate language. This would also be useful in situations found in South Asia, where some L-varieties are associated with H-varieties that are not in fact their closest genetic ancestor; for example, eastern varieties of Hindi (Bihari dialects, etc.) that have long been noted to have descended from eastern apabhramsas but are treated by their speakers as being dialects of standard Hindi; one could make the case that Sri Lanka Tamil may also be more closely related to Malayalam than it is to Tamil, but not in the minds of its speakers. And it seems to be the case that Swiss German was once consensually agreed to be in a diglossic hierarchy with Standard German, but that this consensus is now breaking down.
Scotton (1986) proposes the terms `narrow' for Ferguson's 1959 version of diglossia, and `broad' (or `diglossia extended') to refer to Fishman's expansion of the discussion. According to Scotton, few truly diglossic (in the 1959 sense) communities actually exist, because to meet the criteria, two conditions must hold: ``(1) Everyone ...speaks the Low variety as a mother tongue." and ``(2) The High variety is never used ...in informal conversations." Unambiguous examples of these are Tamil, Lëtzebuergesch, and Swiss German. Britto (1986) proposes the terms `Use-oriented' (or diatypical) and `User-oriented' (or dialectal) diglossia to refer roughly to the same dichotomy others have also attempted to define.
Fishman's 1980 taxonomy of ``kinds of linguistic relationships between H's and L's" is worth stating in full:
(a) H as classical, L as vernacular, the two being genetically related, e.g. classical and vernacular Arabic, classical or classicized Greek (Katarevusa) and demotiki, Latin and French among francophone scholars and clergy in earlier centuries, classical and vernacular Tamil, classical and vernacular Sinhalese, Sanscrit and Hindi, classical Mandarin and modern Pekinese, etc.
(b) H as classical, L as vernacular, the two not being genetically related, e.g. Loshn koydesh (textual Hebrew/Aramaic) and Yiddish (Fishman, 1976) (or any one of the several dozen other non-semitic Jewish L's, as long as the latter operate in vernacular functions rather than in traditional literacy-related ones (Weinreich, 1980).
(c) H as written/formal-spoken and L as vernacular, the two being genetically unrelated to each other; e.g. Spanish and Guaraní in Paraguay (Rubin, 1972), English (or French) and various vernaculars in post-colonial areas throughout the world ....
(d) H as written/formal-spoken and L as vernacular, the two being genetically related to each other. Here only significantly discrepant written/formal-spoken and informal-spoken varieties will be admitted, such that without schooling the written/formal-spoken cannot even be understood (otherwise every dialect-standard situation in the world would qualify within this rubric), e.g. High German and Swiss German, standard spoken Pekinese [Putonghua] and Cantonese, Standard English and Caribbean Creole. (Fishman, 1980: 4).
These differences range beyond the obvious ones of genetic vs. non-genetic relationship, and in fact have to do primarily with power relationships in the societies characterized by them. Various scholars have proposed that extended diglossia is usually unstable, unless certain conditions having to do with power are not met. Classical diglossia, usually thought to be more stable than extended diglossia, can also be shown to be unstable under certain conditions. It may also be the case that the type of diglossia in question may also itself change, i.e. a narrow kind of diglossia may be replaced by a broad form without much overt awareness on the part of the speech community.