If there were a legal definition I am sure the rabid moneysupermarketers would come out foaming about nanny state paternalism or eurocratic interference. Fortunately no such legislation exists and outside biological taxonomies there is no undisputed canon.
It is more often distinguished by recipe - from your description it seems you were over specified - those sliced peppers are just showing off and if any nestling is taking place then you have been given too much lettuce. A prawn cocktail contains the bodies of small prawns and a pink sauce. I would be outraged if I ordered a prawn cocktail and received some minilobster with any legs or feelers still attached and anything more than a single leaf and a single tomato slice. You don't want the palate to have to fight to savour the bouquet of the Creamola Foam.
The disputed canon:
prawns are bigger - shrimps are smaller
prawns are freshwater - shrimp are seawater
-neither of these is universal.
Biologically, prawns don't neatly tuck in their shoulder pads. This may help for when they are trying to take on Gojira
http://www.youtube.com/watch?v=O2mbsfAQeS4