Technically they are different animals, a prawn has a thinner body and longer legs. Also prawns generally swim in fresh water with shrimps in salt water.
In terms of food in the UK we tend to use the prawn for the larger examples and shrimps for the smaller but in the US they tend to use Shrimp for any thing.
Here is a more technical explanation....
Prawns are edible, shrimp-like crustaceans, belonging to the sub-order Dendrobranchiata. They are distinguished from the superficially similar shrimp by the gill structure which is branching in prawns (hence the name, dendro="tree"; branchia="gill"), but is lamellar in shrimp. The sister taxon to Dendrobranchiata is Pleocyemata, which contains all the true shrimp, crabs, lobsters, etc.