Vi is a text editor created for Unix by Bill Joy in 1976. Its name is short for for visual mode, as it was a originally only a visual interface for ex, a line editor created by Joy and Chuck Haley. Its name has spawned the backronym visual interface.
Vim (Vi IMproved) is an expanded clone of Vim created by Bram Moolenaar in 1991.
Neovim is a form of Vim that goes ever further in modernising Vim, adding many features but most notably LSP support.