In the UK we use the ISU music for testing and competitions no matter the level. Only exception is the Riverside Rhumba I think!
Some ISU tunes that double up...
Waltz = Prelim Waltz, Dutch waltz, Willow waltz, European Waltz
Foxtrot = Prelim Foxtrot, Foxtrot
Blues = Rhythm Blues, Blues
Tango = Canasta Tango, Fiesta Tango, Tango
Westminster Waltz = Golden Skaters Waltz, Westminster Waltz
Rocker Foxtrot = Swing Dance (US does this to the Foxtrot though), Rocker Foxtrot
We mostly use the ISU music for club dance intervals but not exclusively. My coach uses the ISU tunes (+Riverside) for lessons often using different tracks for each dance initially but then using a bit more variety after a while especially as she is trying to get me to compete solo dance.
If it is correct tempo for the dutch it would work fine for the Willow.
Maybe your coach just prefers to teach the 2 dances to 2 different tunes to save any confusion unless there is a necessity to do otherwise for testing or competing?