I assume you're talking about physically logging into different machines since cmd-k is a shortcut key for the terminal and will work regardless of which machine you ssh into.

cmd-k works well for me since I don't think I've personally logged in directly to a non-Mac *nix-like system in 15+ years.

vim is different since it requires configuration on the same system.

This superuser explains some subtle differences between the two commands: https://superuser.com/questions/819593/what-is-the-differenc...