In the days when there were legal controls on public road services and everything had to be licensed, there was a distinction by the minimum fare charged, under the Road Traffic Act 1930. Now this was set at the time at 1 shilling, which would be 5p today, and it was NEVER changed until road service licences were abolished in 1986. So things went from when this would take you a long way, to when it was under the minimum fare charged by most bus companes.

The seating used generally determined whether a vehicle was obviously bus or coach. For a long time seats for two with no division were buses, and separate seats with armrests were coaches. There were a range of upholstery types but a useful distinction was buses had hard seat BACKS (ie what you faced of the seat in front), whereas coaches had them upholstered.