Trigger vs Gate vs Clock

A trigger is indeed a high voltage during a short period of time and then returning to zero, a gate is basically a trigger with a longer duration. A clock is just a (ir)regular sequence of triggers. Midi clock for example consists of 96 triggers during the duration of 1 quarter note. So if you send a series of triggers from a squarewave lfo into the midi clock divider module you will see that it's output is much slower than the incoming triggers because the module will count 96 triggers before sending out 1 trigger and/or 3 triplet triggers.

The beat divider module (and other dividers) are great for getting the various clock rates you want for triggering different parts - in the AE the trigger is +5V, 0 volts is no trigger. A trigger is really for percussion, but if you trigger an envelope module then obviously you can generate a CV signal for modulation or anything really! A trigger only becomes a gate by sustaining to my mind, like holding the key down on the keyboard. Some confusion can be caused by the length of the trigger signal being called the gate time, which is adjustable on most arpeggiators, drum machines etc. This can be to make sure you trigger the relevant piece of gear/ sound reliably, but more often to get the musical effect desired from (very) staccato through to legato sound.