It is not possible for a pig to turn into a wild boar, because the two animals are different species. Pigs and wild boars both belong to the same scientific genus, the "sus" genus. However, domestic pigs are known only by the genus name, while wild boars are distinguished from them with the scientific name "sus scrofa".
Pigs were originally domesticated from some species of wild boars approximately 10,000 years ago. Those domesticated animals were first brought to the U.S. in 1539 as part of the Spanish colonization of Florida. Some of those domesticated pigs eventually escaped and became feral. Once in the wild, those feral pigs developed longer hair and sometimes even tusks, giving them an appearance closer to that of the original wild boars of Europe and Asia. However, while some hunters refer to the offspring of those feral pigs as "hogs," they are actually still a variety of pig. Virtually all the feral pigs referred to as "hogs" in the U.S. today are really pigs, though a small number of Eurasian boars were brought to American in the 19th century by private landowners and hunters wishing to hunt them. These true boars have, over the years, bred with American wild pigs to create a hybrid species.