STAR to nearby airport

Recently while returning from a trip I was heading to my home base, which is
a class D airport. I was handed off to the local tracon, which has a class C
airport, and was issued a clearance to follow a star that led to a navaid
near my destination. However, the star was for the class C airport, not my
destination. The class D airport is well outside of the class C airspace but
inside the area covered by the tracon.

I happened to know the star was for the class C airport, and followed it
appropriately. However, in the Jepps it is listed under the class C, and not
my destination.

I have never encountered this before even in a busy radar environment- is
this a common controller technique for arrivals?

If I had been unfamiliar with the area and approaches, this could have
caused a few moments of frantic chart flipping. Besides, the star did not
list my destination airport as one of the transitions, although a nearby
navaid is the IAP for several approaches.

Since my last clearance was the star into the class c airport, if I had gone
nordo, would I have been expected to fly to the class C airport listed in
the star and do an approach , or should I do an approach to my destination,
even if not listed in the star?