Thunderbolt refers to socket or plug, or both?

Solution 1:

Actually it's neither.

The plug is a USB-C connector.

The socket is a USB-C socket.

Thunderbolt 3 is the specification that details the pin-layout, signals, cable requirements, power and protocols that, amongst other things, makes it possible for those connectors, plugs and cables in the picture to enable the functionality mentioned.

You can read a more in-depth description in this technology brief:

https://thunderbolttechnology.net/sites/default/files/HBD16235_Thunderbolt_TB_r05.pdf

The brief is a bit more technical than just the illustration, but still at a level that can be understood without being a computer engineer.