What's the name for [the other kind of planet] in a binary star system? This XKCD what-if talks about rainbows on planets in a binary star system.   It points out that there are two types:

circumbinary planets, where the planet orbits far from and around both stars
[the other kind of planet], where the planet orbits one of the stars and the other star is distant.


What is the proper name for [the other kind of planet] ?
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