UTC is the civil time scale. GMT is a time zone name for the British Isles in winter. They match in winter in London, and they are not the same thing. The live clock is this computer. If it is more than 30 seconds off UTC, the site says so once.
History
The 1884 International Meridian Conference set the prime meridian at Greenwich. Offsets worldwide still talk as if that line is zero. Coordinated Universal Time took its name in 1967, a compromise between English CUT and French TUC. The leap-second form of UTC began on 1 January 1972. BIPM publishes the scale. This page is a civil clock, not a BIPM bulletin.
GMT
Greenwich Mean Time is the civil name for UTC+0 in the United Kingdom and Ireland in winter. In summer those islands use British or Irish summer time, UTC+1. The hour on a London winter clock matches UTC for ordinary use.
Leap seconds
UTC is atomic. Earth rotation wobbles, so IERS can insert one leap second, usually 30 June or 31 December. The last one was 31 December 2016. In 2022 the CGPM voted to stop leap seconds by 2035. Local zones do not invent their own extra second.
This site
Tokyo is Asia/Tokyo, not UTC+9 forever. Governments change the offset. The converter, map, and city clocks read those names.
This clock
The digits follow this device. A one-off fetch of UTC from TimeAPI.io or Cloudflare only warns if the machine is more than 30 seconds off.