At 18,000 miles, during my service B, MB recommended that I change my front brake pads. I authorized the service, and $255 later, my car was ready.

I'm looking at the invoice, it says:
B29C REPLACE FRONT BRAKE PADS, C240, 2001 & NEWER 30000 C2
1 004-420-05-20 BRAKE SHOE
2 220-540-07-17 SENDER UNIT
1 01901 BRAKE KIT

I just wanted to make sure I got the right pads. Does the C240 share the same pads as the C32?

Those are the correct brake pads.
The dealer would not install the incorrect pads, and the incorrect pads would not fit.
The sender unit is the wear sensor
and the brake kit is most likely anti-squeek paste.
You got the correct pads, those pads can be used on many differnt modles such as the sl, s, m and so on.
Tom