Janet/Jessie is probably the most common. I've never been able to find out how and why Jessie became regarded as an equivalent to Janet, because their derivation is unrelated, but when I mislay a Janet, I very often find her as Jessie, and vice versa.
Jane/Jean and variants
Jane/Jean and Janet are also often said to be interchangeable, but in my experience this is unusual. I have found more families with both a Jane/Jean and a Janet than I have ever found instances of a Jane/Jean turning up as a Janet.
Hector/Eachainn (no idea why)
Margaret/Marjorie and variants
Peter/Patrick
Elizabeth/Betsy .... Betsy/Beatrice .... Beatrice/Elizabeth
Ann(e)/Nan .... Nancy .... Agnes
Elspet is the Scottish spelling of Elizabeth, and Isabella is originally the Spanish version of Elizabeth, but over time that equivalence has been lost and it's unusual now to find an Elizabeth as Isabella or vice versa.
For umpteen more examples, and some explanations, see
https://whatsinaname.net/