[JoeF]

"Kite" or equivalently "kite system" ever consists of anchor set, tether set, wing set.
And anchor set may also be collection of wings. Anchor set and wing set are coupled by tether set.

Here are some activities involving kiting:

Kite boarding, kite surfing, water kiting, has system anchor being human and board sliding on water. During "jumps" the system become an instance of air kiting, which see.

Land kiting has kite system anchor set sliding or rolling on land; or anchor set may simply be fixed to the land (even so for human as anchor coupled with the land--standing, running, walking, sliding). if anchor leaves ground for a jump or air travel, then the system becomes instance of air kiting, which see.

Snow kiting has kite system anchor set sliding or skiing on snow. During episodes of full "air" then there is a morph to a form of air kiting.

Ice kiting has kite system anchor set sliding on ice. During leaps into air there is a change to a form of air kiting, which see.

Powered-anchor kiting has many forms. Say power boat towing a wing (manned or not). Etc. Air tow of wings (manned or not). Other forms of powered anchors where the powered anchor is winching or moving (in soil, water, air).

Air kiting (hang gliding with kite hang gliders fits here; non-kite hang gliders stretch the word deal by examining the tendons of the hanging pilot as the kite tethers). Air kiters slide (glide) on air inclined paths; both the anchor set (pilot mass, harness) and the wing set slide (glide) on air. During ground handling there can be formats where the system becomes instance of land kiting or water kiting

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Kiting is a huge activity realm. Hang gliding is a form of kiting: air kiting type.