Absolutely not, not in any traditional society.[1] The elite are governors; the super-rich are merchants. Those super-rich are what the term "middle class" used to refer to.
In a capitalist society, though, it's next to impossible for super-rich to not be part of the elite. It's right in the name. People with capital are running the show.
Capitalism was invented to manage the slaver's business model in the US, so as long as "the elite" is defined to include the economic class of slavers, the US groups the super-rich and the mere business successes largely within a single discourse. I see this as an aspirational application of hyperdescent[1] by the slavers to elevate themselves in the US's emerging power structure, since I highly doubt the (pre-existing) super-rich would have said "the violent hicks? Yeah they're with us" as the US's self-conception was developing.
Absolutely not, not in any traditional society.[1] The elite are governors; the super-rich are merchants. Those super-rich are what the term "middle class" used to refer to.
[1] Phoenician city-states may be an exception.