So what is the difference between Vespers and Great Vespers?
The structure of both services is similar, but the Small Vespers does not have an entrance or any readings from the OT. Great Vespers does.
Since there is no entrance in the Small Vespers, it is customary to keep the church more subdued and simply read or intone the "Gladsome Light"; whereas, in a Great Vespers, all the lights/candles are lit brightly and the hymn is chanted by the full choir.
Also, since there is no entrance, the priest does not put on the phelonion
-- only the exorason
In the Byzantine tradition, one can add an Artoklasia
(blessing of the five loaves), often with a solemn procession of the festal Icon, near the end of the Great Vespers. Not so for a Small Vespers, of course.
Finally, in monastic settings (e.g. Mt. Athos), they tend to chant all of the hymns during Small Vespers in the syndomon
(fast) style, so that each syllable has only one note. During Great Vespers, everything is done argo-syndomo
(slow-fast), or sometimes even in argon
(slow), which is much more ornate. Same goes for a lot of parishes.
Typically, one only celebrates Great Vespers on the eve of a Divine Liturgy; Small Vespers is for every other day.