[G-CPTN]

Here in the UK, buses will usually have certification for 'standees', whereas coaches (as above, designed for longer distance travel at (possibly) higher speeds) are unlikely to have any provision for standing passengers (and should now be fitted with seatbelts).
Buses are likely to be fitted with 'rapid-action' folding doors (and may have more than one entrance/exit) whereas coaches probably have close-fitting side-hinged doors (OK some luxury coaches for tour-operator use might also have multiple entrances/exits) designed to minimize wind-noise (and retain heat).
Buses are more likely to operate 'on demand' with passengers collected from staged stops and paying (sometimes the driver) for a short indeterminate part of the vehicle journey, whereas coaches more likely carry pre-booked passengers for longer (and maybe total) sections of the journey and the driver is unlikely to handle money.
Coaches typically have individual overhead lighting for each seat (and maybe a dedicated fresh-air outlet).
The driver may also have a PA system, and the vehicle will be fitted with side and/or rear underfloor luggage lockers (accessed externally).