Byo-Yomi
Byoyomi (秒読み), a Japanese go term adopted into English, is counting out seconds (aloud) by the timekeeper (or the clock) to help players avoid consumption of their last few time periods (byoyomi periods), especially in Japanese Timing.
Players are in byoyomi from the point on this is done for them.
Any other usage of "byoyomi" is strongly deprecated.
It neither is a time system (even if used by Japanese Timing) nor an overtime (even if being in it means time pressure):
Time restrictions change in no way when players enter it.
It's a service to them.
See also