The rules say the following regarding musical instruments (PH p.154):
Each type of musical instrument requires a separate proficiency.
Since this text is an annotation for the equipment list on the same page, one might assume that a “type of musical instrument” refers to entries from the list. So “flute”, “horn” and “pan flute” would all be distinct proficiencies.
However, Pipes of Haunting and Pipes of the Sewers both require that (DMG p.185):
You must be proficient with wind instruments to use these pipes.
This suggests that the much broader class of “wind instruments” is a “type of musical instrument” for the purpose of proficiency.
Bards choose proficiency in three musical instruments. What are their choices?