The difference in the English and Spanish names has a bit of history behind it, rather than being a mis-translation. The name goes back much farther than we might suppose, considering the town was first settled only in the 1920's.
It was 1826 that retired Lt. Robert William Hale Hardy of the British Royal Fleet was sailing along the coasts of Sonora and Baja California searching for pearls and precious metals in the sailing ship La Bruja (The Witch). He baptized the point Rocky Point and it was identified as Rocky Point on marine maps until General Lazaro Cardenas (who was to become president of Mexico in the 1930's) changed it to Puerto Punta Penasco (Port Rocky Point). Americans dropped the Port, and Mexicans the Punta.
During Prohibition there sprang up along the border bars, clubs, hotels, and casinos, which offered thirsty Americans beer and liquor and, in some cases, women and gambling as well. Then John Stone, who owned the Hotel Cornelia in Ajo, decided to build a hotel-casino farther south, near the sea, to combine the money-making potential of fishing with that of alcohol. He dug a well for potable water 20 kilometers from the coast and recruited a number of fisherman who were willing to risk living in harsh conditions. So was born the town of Puerto Peñasco.
Rocky Point (Puerto Peñasco) has become very popular as a destination for travellers with trailers and RV's, assisted by its very close proximity to the US border, at one and a half hours form the border crossing this is southern Arizona's closest beach. The Sonoran town is located on a stretch of the Sea of Cortes that is rich in marine-life, making it popular with fishing fanatics.