Most professional piano entertainment are able to play in the style of jazz to varying degrees, without actually being a legit jazz pianist. For many clients; Frank Sinatra and Michael Buble are jazz, and those are the melodies they want to hear. Maybe they want to hear some light FM melodies sprinkled in. Other clients want to hear classic old time Jazz at their corporate event and these clients would require a legitimate jazz trained pianist. Both styles are completely valid for classy cocktail music, and to be brutally honest, the majority of the guests will not know the difference unless it’s pointed out to them.
From the musician’s point of view, it takes much more training to achieve the status of a true jazz pianist, and as such, they get more respect in the music world. Even cocktail players that play “jazzy”, or “in a jazz style” really have a limited jazz vocabulary and can’t really “hang” with the straight up jazz crowd.
From the standpoint of a client looking for background music at their event, in our experience, it’s usually not important to them whether they are hearing legitimate jazz improvisation, or “jazzy” version of a melody. Just because it’s not straight up jazz doesn’t make it unsophisticated.
As for the pricing, with any professional party entertainment you are paying for professionalism, experience, musicality, and a classy presentation that can float in the background, adding ambience and being complementary to party chatter. Whether it’s “cocktail music” or true jazz, the cost is generally going to be the same.