Well, yeah, British usage has some hangovers from pre-capitalist class structures wherein the nobility constitute the upper class, and what became the capitalist upper class is part of the middle class between the nobility and the peasantry.

Whereas American English mostly, when it adopted class language, got it from traditional discussions of capitalist class structure, but its since evolved to where frequently "middle class" is used to mean "middle income" (solidly in the working class in the classical divide of classes in capitalist society), and the traditional capitalist middle class is "upper middle class" (or sometimes even "upper class"), and the capitalist upper class -- the owners of capital who rent labor -- are mostly just not discussed at all as a class of people, but as abstract institutions if at all.