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There is a long-standing identification of a need to differentiate various public transport offerings. The most usual ones needing some kind of separation are: tourist buses, which may be coaches, double deckers etc.; and long-distance buses, usually operated by coaches. See also my unanswered question on OSM Help from 5 years ago

The latter category are a major form of long-distance travel in Estonia, Latvia, Malaysia, Spain and Argentina; but also widely used in Britain and Ireland. Greyhound buses used to be a significant factor in long-distance travel in North America. Virtually all of these have different stops in different locations (I was flummoxed at the main bus station in Kuala Lumpur because I assumed the bus I wanted was a coach when it was actually a bus and departed from the underground platforms used by regular bus services).

Various kinds of “service bus” public transport may also be served by coaches, my local one is an express bus, the Red Arrow, but these usually stop at the same stops as ordinary buses.

In this context “coach” really refers to long-distance express or non-stopping services, and any relevant tag should perhaps take that into account (i.e., service may not always be a coach). Note that, particularly for tourist buses, there are also bus stops labelled “Set down only” which will never be part of an bus route. This stop pretty much follows regular TfL signage though, with the exception that the roundel appears to be a different colour. Dedicated coach stations seem to be fewer these days, with most serving bus stations with both “service buses” and long-distance services.