I believe that Great Vespers is Vespers done the night before a Liturgy, which is why we use it on Saturdays. Occasionally when we have weekday Liturgies such as Annunciation, we'll have Great Vespers on other days as well.
Great Vespers is actually not determined by Divine Liturgy, just the size of the feast. Great Vespers is done during each day of Bright Week because
each day is Pascha all over again. Pascha is a 3-layered feast (unlike the other great feasts, which have only two layers): the feastday/afterfeast (which all the major feasts have), the general festal period (which all the feasts have), and a 1-week intense repetition of the feast (unique to Pascha).
Speaking from my working knowledge of the Russian Vespers tradition:
Daily Vespers- No entrance of the clergy before "Gladsome Light"
- Always (iirc) only one verse for the Prokeimenon (since this is almost always the Prokeimenon of the Day [of the week])
- Augmented Litany at the end of the service, but before the Dismissal
Great Vespers- Clergy entrance before "Gladsome Light"
- Often, though not always, a 3-verse Prokeimenon
- Augmented Litany following the Prokeimenon (and any readings, if prescribed) and before the prayer "Vouchsafe, O Lord..."
- Litya often, though not always, preceding the Aposticha
This is a pretty good list, except that the most commonly celebrated Great Vespers (Saturday nights), at least in the Greek practice, only has a 2-verse Prokeimenon.
All this said, 2 notes:
1. As Arimethea noted, all Bright Week services are radically altered by the constant intense celebration of Pascha. Especially in the Greek-tradition practice (Antiochian, EP, Greek, etc.), the beginnings of the services are changed, the Psalms are entirely eliminated, the endings of the services are changed, etc. - all this in addition to more minor rubrical changes (such as: deacons are not to use the deacons' doors, only the beautiful doors; in many traditions also the priest is the only one who censes during the week; etc.).
2. One last note: there is also a "Small Vespers," which is different than regular daily Vespers in one detail: it is daily vespers done before a vigil (the vigil containing a Great Vespers). Minor detail.
