Hey Cathy,
No, unfortunately, white shrimp are Penaeus vannamei (Pacific white shrimp) one of two species that make up about 80% of all farmed shrimp stock (hence the relative inexpensiveness of the product); The other species is Penaeus monodon (giant tiger prawn).
Gulf shrimp have a distinct flavor profile, being wild stock, which some people find to be an acquired taste. Some describe it as having some tinges of iodine (actually bromine) for lack of a better description. Also gulf shrimp are sometimes called "gulf brown shrimp" - cause their shells are beige-pink tinged in color.
In the U.S. markets, it's difficult to find wild shrimp these days - typically you're looking either for "Texas" gulf shrimp or wild Florida shrimp.
While P. vannamei and P monodon are tasty, it's the same taste differences as eating farmed vs wild salmon (aside from the antibiotics, color-added foot pellets, increased levels of dioxins, PCB's & heavy metals and differences in nutritional value).