Digital step sequencer
A digital step sequencer is a step sequencer that uses a microprocessor and RAM to remember and play back sequences of notes, generally in short looping patterns of sixteenth notes. Although it's digitally controlled, its output usually consists of analogue CV and gate signals.
Fundamentally, a digital step sequencer is designed to work like an analogue step sequencer with extra features. While an analogue step sequencer can play a looped bar or so of equidistant notes, usually eighth notes, a digital step sequencer can memorise and play back several such patterns, usually of sixteenth notes, then chain them together to form a whole song. This is the approached used by the step sequencers within the TB-303 and TR-808, and certainly contributed to the sound of acid house.
Digital step sequencers are based on the principle that a piece of music consists of a few repeating short phrases. This is in contrast to a regular digital sequencer, which uses the exact same technology, but conceptualises the music quite differently, as a single long list of notes that can each start and stop at arbitrary points along a finer grid, and don't necessarily repeat at all.
A digital step sequencer tends to use the same finer grid as other digital sequencers, at 24 pulses per quarter note, but largely ignores its advantages, merely incrementing to the next sixteenth note every time it receives 6 more pulses.