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Bilingualism and diglossia are different. Bilingualism is about two languages you know having essentially the same functions, such that it is easy to translate from one to the other. Simultaneous translators are bilingual, or even trilingual as the United Nations requires, because they need to be able to say exactly the same things in their different languages.
With diglossia, however, what you find is a child first learning one language and speaking it at home, and then later on, maybe at school, transiting to another language which is used for less basic things. The end result is not two separate languages that exist in parallel, but a single competence, where ground-level things are done in the first language and things to do with school, or the modern sector, in another. And since each of these languages is bound to its context, translation is not easy.
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Peggy Mohan (Wanderers, Kings, Merchants: The Story of India through Its Languages)