The technical term for it is "voices". Its distinct from instruments which can play more than one note at a time (polyphony), and things like piano which have 2 staves (one for each hand); or multiple instruments on the same stave. 1 instrument can have several voices, and some of those voices can play more than one note at a time.
Think about, as an example, pitched instruments.. A bass guitar's score could be presented as one voice, ie a normal bass line which might/might not be complicated or fast; and might contain double or triple stops eg chords (or 4 or more). But it could also be presented as 2 voices if use of open strings plus another line much higher up the fretboard were played at once - eg Dune Tune by Level 42.
Turning to non-pitched instruments, the bass drum may well be presented separately (and therefore include rests in its voice) as your example shows; but equally valid is to consider the entire drum kit as one 'voice' with many parts which can be played simultaneously eg hi hat, snare and bass drum all together.
There is no particular convention for when an instrument is split into different voices or remains as one, in notation often the most simple presentation might be written out, or it might be written with voices if other parts (eg in a group when other instruments are playing) lend themselves to the composition/presentation showing them. Or it might be because something is rewritten for another instrument, eg some piano music score is for pop tunes, where the piano is playing the main line which was once the bass guitar and some of the guitar parts, etc etc.
