A second-order 12db/oct low-pass has a 12 db/oct high-cut, and some unknown (hopefully minimized) amount of ripple in the passband. There's an advantage in naming filters after the more "interesting" part of the spectral response (eg. a second-order 12 db/oct highcut) where you're doing the most sculpting of the spectrum, where different filter orders behave differently, and different designs have different levels of stopband leakage. Though on the other hand, there's some benefit in naming filters after what's passed.
