Audio sequencer

Digital audio workstation (DAW), Hard disk recorder — an class of audio software or dedicated system primarily designed to record, edit, and play back digital audio, first appeared in the late 1970s and emerging since the 1990s. After the 1990s–2000s, several DAWs for music production were integrated with music sequencer.

Loop-based music software — a class of music software for Loop-based music compositions and remix, emerging since late 1990s. Typical software included ACID Pro (1998), Ableton Live (2001), GarageBand (2004), etc. And now, several of them are referred as DAW, resulting of the extensions and/or integrations.
Its core feature, pitch/time manipulation allows user to handle audio samples (loops) with the analogy of MIDI data, in several aspects; user can designate Pitches and Durations independently on short music samples, as on MIDI notes, to remix a song.

This type of software really control sequence of audio samples, thus, possibly we can call it "audio sequencer".

Phrase sampler (or phrase sampling) — similar to above, musicians or remixers sometimes remixed or composed songs by sampling relatively long phrases or part of songs, and then rearranging these on grooveboxes or a combination of sampler (musical instrument) and sequencer.

This technique is possibly referred as "audio sequencing".

Beat slicing — before DAW became popular, several musicians sometimes derived various beats from limited drum sample Loop by slicing beats and rearranging them on samplers. This technique was popularized with the introduction of "beat slicer" tool, especially the "ReCycle" released in 1992.

Possibly it may be one origin of "audio sequencing".