OK it's a word thing

The aircraft moving at less than M1.0 is sending out Pressure Waves. These are of low impact. As the aircraft goes faster the waves pack up into a denser front, a Mach Wave. This forms first nearly on the nose of the aircraft at M1.0, then bends back into a cone, a Mach (Wave) Cone. Meanwhile, on the aircraft, speeds are reaching over M1.0, and forming local shock waves which brings the flow back to subsonic

It is just conventional to call the pressure waves that are very strong and/or attached to the aircraft "shock" waves rather than strong Mach waves. They are generated by the aircraft and are therefore at maximum effect on or close to the structure - wings, fuselage etc.

The one that doesn't touch the aircraft, if it has a blunt nose, is the Bow (Shock)Wave, and that is because the air is brought to rest and heated and M1.0 in the hot air is faster than the aircraft is going so the Bow Shock backs out a little.

As to timing, the aircraft is not going to catch up properly with the bow shock wave until it reaches M1.0, and even then will be held off a little, so it doesn't affect the airflow pattern until a little after M1.0

You can see from the sequence in Chap 13 how the bow shock doesn't appear until after Mfs1.0