Lightning chess or “blitz chess” typically refers to 5-minute chess. Each player gets 5 minutes for the entire game. There may or may not be a few extra seconds per move with a Fischer clock. Usually there is no requirement to write down the game on a scoresheet. And usually it is allowed to “take the King” if your opponent leaves their King en prise.
Blitz chess is a particular type of “rapid play chess”. 10-minute chess is often called “allegro chess”. 15-minute chess is often called “rapid play”.
Related Chess Rules Topics
Read more about these related chess rules, chess puzzles, and other chess tactics and strategies: