A one-to-one correspondence is an alternative name for a bijection between two sets, but to what does the term 'correspondence' alone refer? As far as I can see, it seems to be another term for 'relation', but I think there must be a difference.
2026-04-08 09:06:51.1775639211
Definition of correspondence
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Not that I ever use this regularly or believe everything that is written in it, The encyclopedic Dictionary of mathematics agrees with your guess. There may not have to be a difference after all: there are lots of synonymous words in mathematics.
What I read leads me to believe that "correspondence" is an older and dustier term for "relation".
If you asked me the answer without the benefit of resources, I would have told you my impression was that it is a synonym for "1-1 correspondence" and that the 1-1 part was usually added for emphasis.