What are some of the most divergent cognate word forms?

Question

I'm looking for examples like this pair:

Russian for 'grass snake' — уж, [uʂ]
Classical Latin for 'snake' — anguis, likely [ˈaŋ.ɡᶣɪs]

These word forms are both masculine nouns in the nominative, and they seem to derive from a masculine noun in the nominative, *h₂éngʷʰis or something like that. So basically we can continuously trace them to a common origin, which is a word form of roughly the same type, with no restructuring, reanalyzing or borrowing along the way as far as we can tell. Yet looking at the transcriptions, [uʂ] vs [ˈaŋ.ɡᶣɪs] are staggeringly different, to the point where these words actually don't share a single sound and have different syllable structures.

What are some examples like this, but between two modern languages?
(Word forms need to go back to the same word form, complete with suffixes and endings, always passing down through first language acquisition, i.e. no borrowings, and need to look and sound wildly different in their modern incarnations, but do not need to mean the same thing.)

Answer 1

Divergent cognates are going to be a feature of any language family (as pointed out in this paper by Larry Trask used in the answer to this question about "mama" and "papa" words), and because of this I think this question is incredibly open ended and subjective. However, I appriciate the opportunity to share some of my favorite etymologies.

Afro-Asiatic is estimated to be a fairly old language family and therefore has a large number of divergent cognates, I personally enjoy the divergence in my own name which I found here.

• English David, from Hebrew דָּוִד (Tiberian Dāwîḏ, originally dōd), meaning "beloved", but originally a kinship term meaning "uncle"
• Mokilko ʔândé, "in-law"
• Tawllemmet idda, "Dad"

all from Proto-Afro-Asiatic *di/ad- with an unclear meaning but it was probably something like "elder".

Indo-European languages, as you and Michaelyus have pointed out, also have words with fun etymologies, and for some reason Armenian tends to show up a lot:

• English birth
• Latin fortūna, "luck, fortune"
• Armenian -աւոր (-awor), a suffix that forms adjectives, with the meaning “possessing, related to”, as in վտանգաւոր (vtangawor, "dangerous"), from վտանգ (vtang, "danger") + -աւոր

all from PIE *bʰer-, meaning "to bear, carry" (English bear is also a decendant).

This one is kind of cheating, because it's a borrowing, but Japanese 蜜 (mitsu, "honey") and English mead are genetically related through Tocharian B mit from PIE *médʰu. They're all kind of similar looking, I know, I just think it's cool.

Finally, I don't think anyone can discuss divergent cognates without mentioning John McWhorter's famous comparison of Algonquian words for winter:

• Cheyenne aa', "winter, to be winter"
• Ojibwe biboon, "winter, it is winter"

From the Proto-Algonquian *pepo·nwi, also meaning "it is winter".

Obviously, this is not an exhaustive list, there are probably thousands more cognates with this level of divergence because languages do weird stuff all the time.

Answer 2

I have an example from Dravidian. The reconstructed Proto-Dravidian word is *caracu 'cobra, snake'. In the South-Dravidian subfamily, word-initial c- is very commonly elided: first to s-, then h-, and then finally it disappears. Elision of intervocalic -c- is also well-attested in South-Dravidian (and especially in Pre-Tamil). Hence *caracu becomes aravu or aravam with the -am noun class marker added, in Tamil and Malayalam.

In the South-Central Dravidian subfamily, this word underwent another major phenomenon, apical displacement. Apical consonants that occurred in the second syllable of a word metathesized to the first syllable, forming word-initial consonant clusters and word-initial apical consonants, neither of which occurred in Proto-Dravidian. Thus Proto-Dravidian *caracu > Proto-South-Central-Dravidian *crācu > Old Telugu trācu (cr- > tr-) > Modern Telugu tācu (with simplification of word-initial consonant clusters in Modern Telugu).

As a result, Tamil aravam, meaning 'snake' and Telugu tācu, meaning 'cobra' or less commonly 'snake', are cognates, both descending from Proto-Dravidian caracu. They share no consonants with each other.