I don’t agree, and I don’t think that is meaningful, mosty because one person can be in so many different income groups in the course of his lifetime. There are also some people who earn respect in other ways while there are others who have a lot of money and no rank. More importantly, there is no system for allocating or recognizing rank. Listen to the questions when pols talk about taxing the rich. First question is what do they mean?
The term you are looking for when a person who has alot of respect, such as honor and prestige excluding money is "social status". Preachers and teachers can fit into this category. "Social class" is based on "wealth, the power one receives with that wealth and the life chances that one has to accumulate wealth. Socio-economic status is a concept to assess status, depending on a person's income, education, and occupation (Understanding Sociology)."
We also have other terms, white collar worker and blue collar worker come to mind.
I'd say there is a system in place for recognizing rank and status.