Flights still have "first class" although many call it business class. I'm sure ships and trains still have similar arrangements. I think it's a mistake to suggest that there is a direct correlation between this and a formalized position in society, although obviously more well off people are more likely to be able to afford better accommodations.

America did not have a formalized class system in the early 1900s, although like anywhere class and wealth were and are interrelated but not entirely overlapping and can have a profound impact on your life and opportunities.