Ambrosia is a substantive built on the adjective ambrotos, which is a-mbrotos, not-mortal. The same negated formation appears in Sanskrit as a-mrta, amrita, and the correspondence between the two is regular rather than a resemblance: the Indo-European root behind mortal, mrta and brotos is the same root, and both traditions negated it to name the same kind of thing. The Greek food of the gods and the Indian drink of deathlessness are one inherited word.
That is a strong result and it is worth being clear about how far it goes. It establishes that the ancestors of both traditions had a term for a substance of deathlessness. It does not establish that they had the same substance, the same story or the same rite, and the two traditions diverge sharply on all three. Amrita has to be won by churning an ocean, and the myth of who drank it is the centre of the account. Ambrosia is simply on the table, with no origin story at all, and the Greek interest lies in what it does rather than where it came from.
Nectar has been read as a parallel case, analysed as a compound of a root meaning death with one meaning to overcome, so that the drink would be the death overcomer. That reading has support and has also been doubted, and it is not on the same footing as the ambrosia and amrita equation, which almost nobody disputes.
The comparison has a third member. Vedic soma and Avestan haoma are also a substance of immortality, but they are a different word, naming the act of pressing, and they belong to an actual rite with actual plants. Ambrosia and amrita name the property; soma and haoma name the process.