What's the name for [the other kind of planet] in a binary star system?
I don't know about names for the planets, specifically, but the orbits are called S-type and P-type:


S-type: The planet orbits around one star, and the host star has a binary companion (i.e., "the other kind" in the XKCD comic)
P-type: The planet orbits around both stars of the binary