When (and where) is there a difference?
What neighborhoods are there where rich people reside who have no more social or political influence than people living in The Projects?
Compared to this one? Nearly all of them. The neighborhoods in Mountain View are filled with affluent people that have no connection to federal politicians and no influence over the FBI at all.
The highest paid government employees earn around $400k [1], foreign diplomats probably earn considerably less (e.g. £150k for the UK's [former] representative to the EU [2], which is the highest-paid ambassador position) but have perks like paid-for private school for children and tax exemptions.
[1] https://www.federalpay.org/employees/top-100
[2] https://assets.publishing.service.gov.uk/government/uploads/...
Money can buy political influence, but that's beyond the reach of lower echelon of wealthy.
The same is going to be true of a lot of people living in Kalorama - they're on "personally know the President" level of political influence or they work directly for someone who does.
It's the neighborhood where Obama lived after his term ended. It's where Ivanka Trump and Jared Kuschner lived during Trump's presidency. That kind of thing.
It's a little different than a standard affluent neighborhood of doctors and lawyers and executives that you might find in any random city in the US.