I have a copy of Met.O.630/AP3340 Handbook of Aviation Meteorology 1960 which I was issued with in the RAF. It uses a sub-title "Warm-sector depression" under the broader heading General Distribution of Weather in a Frontal System.
For PPLs I rather like Brian Cosgrove's book; Pilot's Weather, a very pracical book aimed at Microlight Pilots. He makes no mention of a Warm Sector Depression but talks of Anabatic and Katabatic Fronts providing lots of pictures of the associated cloud formations..
As UK weather is predominately associated with frontal depressions, I think the associated weather is relevant to the private pilot.