I think this is correct for the most part, but if “transit mall” really is still specific to American English, then it absolutely can allow private cars. I drive down the transit mall I mentioned on a regular basis. It’s a pleasant experience if you don’t mind the lower speed limit and having to watch for pedestrians darting across. Also note that most laypeople are unfamiliar with the term; it’s mostly jargon from urban planning and transit advocacy circles.
As I understand it, the concept of a transit mall basically started with the Portland Mall in Portland, Oregon. The design prioritized public transit and tried to be as pedestrian-friendly as possible while still allowing some private motor vehicle use. It was so successful that other cities tried to emulate it. Some cities, like San José, had to water down the design and allow through traffic by car, while others have managed to prohibit car traffic entirely.
Regardless of any local quirks, the primary defining factors are improved public transit facilities (similar to BRT) and pedestrian friendliness (similar to a bus station). This distinguishes transit malls from something like San Francisco’s Market Street. Nowadays, this street also prohibits private cars except for some short maneuvers, but it’s still a monster of a street that you’d be foolish to jaywalk across, so it isn’t a transit mall. It also isn’t currently tagged as a busway, but I suspect this has more to do with how disruptive it would be to retag this street. Not only would the city’s main thoroughfare disappear from osm-carto, but it would also probably catch out a lot of routers. This happens to be the most important street in the whole world from the perspective of VC-funded mapping and autonomous driving startups, not exactly the sort of software shops that are thinking about pedestrian or transit facilities.