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'Two of a kind' means a pair that are just alike. It does not speak to the commonality of the item or persons.
I've not heard two of a kind used like that, but it's interesting to hear 'of a kind' scales logarithmically.
I thought “two of a kind” meant that they were the same. Like you and your friend are two of a kind, liking the same things, having similar personalities, etc.
Yes, and such pairings occur way more frequently than "one of a kind".
The saying "two of a kind" is saying that the similarity of the pairing pairings are uncommon enough to stand out from a random pairing.
But at the core it is a comparison of similarities, not about frequency. One of a kind just means there isn't anything similar.