The long distance coach to e.g. Leicester starts at the same place, but takes the motorway and doesn't stop until it gets to Leicester. Maybe it will then continue to another city, e.g. Manchester. (I've done this trip.)

The OP took intercity / intertown "local" buses, but they stop at many larger villages and towns along the route. This is much slower, as it usually involves leaving the large road and winding through narrow roads to the centre.

Example map for the Leicester-Loughborough-Derby bus, showing a fair number of stops, where a coach service might make 1 stop between Leicester and Derby: https://www.trentbarton.co.uk/services/skylinkderby/maps-and...