The vi editor has three primary modes: command mode (default), insert mode (for text entry), and last-line mode (for commands like :wq). There is no 'preserve mode' in standard vi. Command mode is for navigation and editing commands, insert mode is for typing text, and last-line mode (ex mode) is for operations like saving, quitting, and global substitutions. The option 'preserve mode' is fabricated and not part of vi's architecture.