Private butler vs private gentleman's gentleman?

There is no such thing as a public butler or a public gentleman's gentleman, so they are never described as 'private'. The difference is that the butler is the senior male servant in a private house, who gives orders to all the junior male staff and has general overall responsibility for them. His special responsibilities are the purchase, storage and serving of all kinds of wines and spirits, and the care of the household silver. you generally only find a butler in a family house of some size, with a whole team of junior servants. The gentleman's gentleman, however, is typically the sole servant of a bachelor living in a serviced flat (apartment). He does the job of a valet, but also the work that in a large household would be done by a footman (e.g. serving at table), a butler (storing and serving drinks) and a chauffeur. The

Butler is a very senior and responsible role in the running of a household. A gentlemen's gentleman is rather like the civilian equivalent of an officers batman, and is more usual as a valet, but carrying out the functions of butler and secretary in a smaller household usually to a gentleman before he marries. Use of public and private with these terms is incorrect, as all are directly employed, unless supplied via one of the many domestic agencies that became increasingly popular to cope with the 'servant problem'.

Private gentlemen/lady can get freaky

Watch Downton Abbey