In Britain, there were different classes of travel from the beginning of passenger service. Recent documentaries have suggested that the Stockton and Darlington Railway was taken by surprise that passengers wanted to pay to travel by train and were happy to travel in empty coal wagons in that direction. Of course some other provision had to be made in the loaded direction, presumably by including empty wagons in the loaded train.
When the Liverpool and Manchester railway opened five years later I think there were three classes of travel from the beginning, First Class that provided the sort of accommodation expected in a stage coach, Second that was more basic but enclosed, and Third Class was basically the open wagon, but with wooden benches to sit on.
The railways encouraged the higher classes of passenger, but the British Government decided that a minimum level of service was required for third class passengers, and passed a law requiring that an all stations train conveying third class passengers had to run on each line in each direction daily. These became known as "Parliamentary" trains and that name persisted well into the Twentieth Century for all stations trains.
By the Twentieth Century, however, third class had improved with enclosed and heated cars with upholstered seats, but carrying more passengers (generally ten in a full width compartment with side doors) while first class had larger compartments seating six or eight passengers. Second class had largely disappeared, except for trains carrying passengers to ferries to The Continent.
In Britain, from the late Nineteenth Century had Pullman parlour cars which provided a higher level of service including food and drink served at your seat. These cars generally had individual movable arm chairs, one each side of the aisle for first class, but being Britain, the same service was provided to third class passengers who had conventional seats in facing pairs two plus one across the aisle.
Pullman passengers paid a "Supplement" to travel in a Pullman above the fare in either class (as well as paying for food and any gratuity to the porter.)
British sleeping cars were run by the railways and were not associated with Pullman. Most of these were compartment cars, the concept of Pullman sections not having caught on in Europe.
So in Britain, the class of travel was independent of whether you used a Pullman car.