Ah, ambrosia...

I ate a lot of that. But it didn't make me immortal, it made me fat. (I'm joking of course - the dish above is named after the Greek myth OP talks about.)

Serious now: I think that the myth refers to both honey and mead, without making a distinction between both. I'm saying this because:

• the myth is considerably old, to the point that it has cognates in Zoroastrianism and Hinduism. It's tempting to say that it's an old Indo-European myth, inherited by both sides (Greeks and Indo-Iranians).
• the Proto-Indo-European word *médʰu can refer to both honey and mead (note how it's the ancestor of both English "mead" and Latin "mel" honey). It makes sense if its speakers - i.e. the people who had this myth initially - didn't bother too much distinguishing both things.
• the item in question is sometimes described as food, sometimes as liquid, and it's rather fragrant.

EDIT: about nectar. Both ἀμβροσῐ́ᾱ→ambrosia and νέκτᾰρ→nectar ultimately mean the same thing: "not dying", "immortal" (check the links for etymological info). As such I think that both names initially referred to the same thing, and only evolved into two different mythological food items later on.