Biologically speaking, they are actually different species, but the names are so commonly used interchangeably as to completely muddle the distinctions. For example, spot prawns are actually shrimp while ridgeback shrimp are actually prawns.
Prawns have claws on three of their five pairs of legs, shrimp have claws on two of their five pairs of legs. Their gills and body shape are different too.
As far as cooking them goes, they are virtually identical and interchangeable.
