The term non-dual (gnyis med, or advaya) is used frequently in Buddhist texts. The term non-duality (gnyis med nyid, advaita) is virtually never used, showing up only one time in the entire Kengyur, in a single passage in the Kalacakra tantra (hooray for a text searchable Tibetan canon!); and nineteen times in the Tengyur, the translations of Indian commentaries.
Thanks for this, Namdrol. I was thinking of posting something similar.
Indeed, the Buddhist usage is almost always "advaya", which means "not two", "not dual" (a-dvi). It is thus an adjective, qualifying some other term. (Being a compound and all, I guess it's technically a bahuvrhi.) This means that the phrase "advaya" is not referring to some thing
in itself, but is describing something.
The term "advaita" is grammatically and semantically different, referring to the abstract notion of "non-dual-ity" (a-dvi-tA). As in most Sanskrit usage of an abstract noun, it does not usually qualify some other term, but refers to something in itself. (Still a compound, I guess it functions as a tat-purusa.) Though one can posit it in genitive relationships to other things, such as the "non-duality of X". Hence, in effect, it is a kind of thing
Since the position of Zen has been brought into the discussion (albeit in a rather clumsy manner), it is worth pointing out how the phrase "advaya" appears in Chinese. It appears almost always as 不二, which is again just "not two", a very clear translation of "advaya". It one wished to express "advaita" (or similar abstracted sense), then one would probably use 非二性 (Xuanzang style translation). However, while 不二 appears thousands of times throughout the Chinese canon, including the Chan (--> Zen) works, the latter term or variants, only appear once or twice from what can be found scanning the entire canon digitally.
So, the Chinese - and I'd warrant the Japanese too - most likely had a clear notion of "advaya" as "not two". Whether or not this is held out in English translations of the Chinese or Japanese works, however, is another matter. But considering that of Chan or Zen practitioners, only a tiny minority use English, one would want to avoid gross over generalizations.