Maybe yes, maybe no?
The lower classes are poor in the sense that they are always at risk. A lower income country… puts citizens at greater risk.
The middle classes are stable. They control where they live, are insured against risk, and plan vacations and retirement. A middle income country… spends enough to reduce crime and effectively regulate, but citizens know they need to take care of themselves.
The upper classes are rich in that they do not need to work but choose what to do. An upper income country… treats citizens well and secures them against (most) poor choices.
Yes, it’s obvious that countries contain a mix of income classes, but isn’t it also obvious that income classes mix via work, daily life and/or family and friends? But it’s also true that lower and upper income countries can talk past each other in the same way that upper and lower income classes can, so that’s still a set of parallels.
My one-handed conclusion is that income changes your choices and risk-vulnerability, without necessarily helping you understand how people in other classes (or countries) make their choices.