as everyone says its a cultural category. it's unseemly in bourgeois republics to be aristocracy but people still want to be above the poors. thus the "middle" is everyone above incontrovertible poverty and theres nothing stopping the ungodly rich or even people in poverty from saying they're in the middle.

the one categorical difference is that the "middle" class doesn't have hereditary titles so in theory a very rich "middle class" family might become poor whereas a noble family is noble no matter their financial situation