The backbeat is the only widely used term for a layer of (or role within) a drum groove that I'm aware of. In most popular music, this role is filled by the snare drum. In jazz, it's filled by the hihat (played with the foot). In 4/4, the term refers to the accenting of beats 2 and 4. It would not include any ghost notes because 1) they're not accents, and 2) they're not on 2 or 4. So, for example, if the snare is playing the backbeat, it is not necessarily the case that all snare hits are part of the backbeat layer. As an extreme demonstration of the concept, listen to Tomas Haake of Meshuggah. While the guitars might seem to be in weird and ever-shifting meters, the backbeat is almost always present on the snare to keep your ear oriented.
There are some other widely used terms I can think of, but none has a specific meaning in the context of drumming the way backbeat does. But FWIW, here they are:
By analogy to a heartbeat, the pulse simply refers to the cadence or steady flow of beats (or pulses) perceived by the listener. Pushes, pulls, and rests should not affect the perception of the pulse. It's all of the on beats, in other words. You could also refer to this as the internal rhythm. Generally, your tempo and time signature should be chosen to reflect the pulse. Polyrhythms are essentially just instances where more than one pulse can be discerned at the same time, although there is usually one that is primary while another is used to contrast against it. As for the term's use in drumming, well... er... In a "four on the floor" pattern (eg: think bebop jazz, disco, some EDM, some reggae), the kick drum is playing the pulse. In a basic rock beat (kick on 1 and 3, snare on 2 and 4), the pulse would be played by the kick and snare collectively. Sometimes the pulse appears on the hihat, ride, or another cymbal if the drummer is riding using quarter notes (or in 8th notes but with clear accents on the quarters). This is common in metal breakdowns. In other styles, sometimes you hear snare side sticks keeping the pulse.
The surface rhythm refers to the cadence of the less significant notes (generally quicker and of shorter duration) laid overtop of the pulse (aka internal rhythm). In popular music, the drummer is usually "riding" on something, be it the hihat, ride, other cymbal, or a floor tom, often in steady 8ths but not necessarily. It's this riding that usually provides the surface rhythm. Ghost notes on the snare would also be part of this layer. This layer affects the groove but is independent of the pulse. You could think of it as being more textural than structural. For a demonstration, listen to Baard Kolstad of Leprous. He almost always maintains a quick and constant 16th note surface rhythm on the hihat and snare while his feet do weird things and his backbeats are often displaced.