As a piano teacher, Marian Paroo interacts with students individually (as is shown with Amaryllis), but Hill, as a band leader, deals with multiple musicians simultaneously. Paroo's piano is definitely a stationary instrument, but Hill's band is mobile. The piano is also fully polyphonic, but most (if not all) of the instruments in a marching band are monophonic.
Paroo and Hill are so different that even with respect to this one similarity (their positions as music teachers), they have very little in common.