Gulf shrimp and Atlantic shrimp are two main subcategories of shrimp. While the simple explanation is that the former come from the Gulf of Mexico and the latter come from the Atlantic ocean, this is not the end of their definition. Indeed, Gulf shrimp are actually shrimp from warm climates while Atlantic shrimp are shrimp from cooler climates. This creates a number of differences between the two crustaceans.
Gulf shrimp reach larger sizes more quickly than Atlantic shrimp do. This difference can be profound -- some Gulf shrimp can only fit 18 to 20 to a pound, while some Atlantic shrimp can have up to 500 per pound. Atlantic shrimp are therefore used more often in things like salads where they are part of the meal but not the main event, while Gulf shrimp tend to be used in things like shrimp cocktail where they are the focus of the dish.
Food and Flavor
Gulf shrimp cannot be raised in fisheries like Atlantic shrimp can. This means that there is a lot more variation amongst Gulf shrimp, as a shrimp's flavor depends on what it ate. Atlantic shrimp, on the other hand, are often raised in fisheries under controlled circumstances, which makes their flavor much more predictable. Any one Gulf shrimp may taste better or worse than an Atlantic shrimp, but most Atlantic shrimp from the same fishery will taste the same.
Habitat and Flavor
The habitat that a shrimp matures in also affects things like its size and muscle tone. This is one of the reasons that Gulf shrimp are so much bigger than Atlantic shrimp -- their ability to swim further makes them grow to larger sizes. This also makes them more firm to bite, as the constant swimming gives them better muscle tone.
There is a lot more effort involved in catching Gulf shrimp in the wild than there is in pulling in a catch of Atlantic shrimp from a fishery. This effort needs to be compensated for in order for everyone involved to make a living, so Gulf shrimp tend to be much more expensive than Atlantic shrimp. What's more, stores of Gulf shrimp have been deteriorating, which has been countered by regulation governing how much shrimp a boat captain can catch. The lower supply of shrimp will therefore raise its price as time goes by.