The term "audio sequencer" or "audio sequencing" seems to be not clearly defined.
Music sequencer, a class of device or music software to record, edit, and play back the music, by handling musical notes and performance information in various forms
Several people tend to use the term "audio sequencer" to refer several kind of "music sequencer" (see external link 1). However, their definition seems unclear (see external link 2).
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".