How does Diglossia differ from Register? This author never defines or mentions "register", nor this Bristol University website on British Sign Language or Reddit.
2.3 Diglossia
Diglossia is a sociolinguistic situation in which two very different varieties of a language are both used in a society, but in different situations. Typically, one is used in more formal or literary situations such as formal writing, university lectures, and news broadcasts, and is learned and encouraged in school. The other is used in conversation, informal television situations, folk literature, etc., and is preferred at home.
In the German-speaking areas of Switzerland, both Standard German and local varieties of German known as Swiss German are used; they are different enough from each other not to be mutually intelligible. Writing is almost always done in Standard German. Standard German is also used for formal speaking situations. Ordinary conversation, however, is normally in Swiss German. For example, a university course uses a textbook in Standard German, and lectures are given in Standard German; discussion after class between the professor and students, however, would be in Swiss German.
Arabic is another example of a language with diglossia. We have mentioned in the previous chapter that an Arabic speaker normally uses one dialect for speaking and another for writing. Modern Greek and the Dravidian languages also show diglossia.
The term 'diglossia' is usually reserved for quite distinct versions of the same language. However, other related variations occur. In English, there is not a sharp division between written and spoken English. I forgot to put on my watch this morning seems to be appropriate in any style of discourse, written or spoken. However, words such as lest, pursuant, or vouchsafe are much more likely to be found in written English, or in English read aloud from a written text. Forms such as isn't, aren't, would've are normal, almost required, in spoken English. In written English, they are regularly written as two words.
Henry Rogers, Writing Systems (2004), p 17.