Upper middle class people are those born into a specific type of family, speaking Received Pronounciation and privately educated. People such as Boris Johnson and David Cameron are upper middle class.
Middle class people are often those who have changed the class they were born into by doing well in school, going to University and entering well-paid careers. People such as Michael Parkinson and the McCanns are middle class.
Well historically you had the upper class which would be described as titled eg royalty and the landed gentry. Upper middle class which I would describe as the likes of Jacob Rees-Mogg, BoJo, DC etc. Middle class those who work in the professions and are defined by their professional status in that they may have been born to working class families and attended state schools eg McCanns. Working class and underclass for the rest

But you can see the above doesn't really work now. Eg Kate Middleton and Megan Markle, Sir Philip Green, the Beckhams and Rooneys of this world.