Yes there is no such thing as a "kitchen pipe" per se. Kitchenpiping is informal (noncompetition) Highland piping, and many Highland Games have kitchenpiping contests, usually held after the Games, at night in a pub etc.

About the names for the various species of Scottish bagpipes, this has changed over the years. In the 19th century, and through at least half of the 20th century, all Highland pipemakers used a consistent naming system for the various pipes; here is the way pipe were listed in various old catalogues from MacDougall, Henderson, Glen, etc

1) Great Highland or Military Bagpipe
2) Halfsize or Lovat Reel Pipe (what we today call "3/4 Pipes", a term never used in the old days)
3) Second Size Reel Pipe
4) Miniature or Chamber Bagpipe (what we today call "Scottish Smallpipes", likewise a term not used then)

Many makers omitted #3 above. In fact, I've not yet found anyone who knows what the difference was between the "Halfsize or Lovat Reel Pipe" and the "Second Size Reel Pipe". They cost differing amounts. Both #2 and #3 above were sometimes offered with bellows, and with bellows would be the equivalent of what we call "Border Pipes" today.

Anyhow, #4 above, what was called "Miniature Highland pipes", what we call "Scottish Smallpipes" today, has had a huge explosion in popularity recently.

These are made both mouthblown and bellows blown, with drones in seperate stocks or a common stock, and in various pitches.

For whatever reason, nearly every modern pipemaker seems compelled to invent their own pet name for their Smallpipes. Gibson calls theirs "fireside pipes", and various other makers use names like "shuttlepipes", "studio pipes", "session pipes", and on and on. Wouldn't surprise me a bit if some current maker would call their Smallpipes "kitchen pipes". Whatever...

Anyhow here are the three common sizes of Highland pipes as made by Glen, Henderson, Lawrie, MacDougall, etc from the early 19th century up through the 1940s, when the smaller sizes ceased to be popular