These are, as far as I know, referring to two different groups that may be of similar purposes but only somewhat overlap. Note please that I'm using the word "group" in the loosest possible sense, it isn't clear at all that these groups act in some sort of concerted fashion as much as they share or have compatible goals/means.
This refers to the fact that politics has not only become a career in itself, but has spawned an entire cottage industry of ancillary jobs: staffer, aide, lobbyist, campaign management, etc. There are a lot of people in Washington D.C. whose financial fortunes are tied up with the current order. Because this group is presumably large and geographically co-located, it creates the impression that it is a culture unto itself: even if Democrats and Republicans are on opposite sides they're both caught up in the same game. To say someone is a member of the "Establishment" is to claim that their opinion is untrustworthy because they have too much at stake in the current order to effect meaningful change.
This refers to a group that only occasionally overlaps the first and is comprised of financial, political, and cultural leaders. Elites influence policy directly through campaign contributions/lobbying/running for office, but also indirectly via cultural means such as media and entertainment. Again, all of this makes it sound like this is coordinated but it need not be: merely the sum of personal and cultural vectors pointing in the same direction. The moniker "elite" also carries class connotations that may or may not hold in any given case.
Why One Might View America in These Terms
One of the most visible political figures is the President. So let's look at the ones during the course of my lifetime:
- Jimmy Carter, exception. Note that he's farthest removed in time from today.
- Ronald Reagan, famous actor
- George H.W. Bush, independently wealthy
- Bill Clinton, wealthy
- George W. Bush, multimillionaire son of a former POTUS
- Barack Obama, possibly the only actual deviation from the pattern since Carter
- Donald Trump, billionaire, household name before running for office
Every single one of them were either extremely rich or famous or both with the exception of Obama and Clinton, the latter of whom was still pretty well-off. Note that losing presidential candidates tend to follow this pattern as well (Hillary Clinton, Al Gore and Mitt Romney being a couple of particularly stark examples). This creates an impression that rather than some unbiased meritocracy the public instead is expected to be grateful to have a choice as to which particular multimillionaire relative/spouse of a former national politician gets to nominally run the show.