These songs have separate entries in the Roud Folk song index (Canadee-i-o is 309, Caledonia is 5543). The tunes of, for instance, Caledonia as sung by Emily Smith and Canadee-i-o as sung by Nic Jones are completely different, though its possible that Nic Jones wrote his own). The lyrics are different, though the plot is only different in respect of the direction of travel across the Atlantic. There is a short discussion of this on mainlynorfolk:

https://mainlynorfolk.info/nic.jones/songs/canadeeio.html

To confuse matters Caledonia by Dougie MacLean is different and When I first Came to Caledonia sung by Norma Waterson is different again.