One alternative English spelling of Pad Thai listed by Wikipedia is “Phad thai.” The variation reflects different attempts to represent Thai pronunciation and romanization using the Latin alphabet.
The dish’s Thai name is ผัดไทย, commonly rendered in standardized romanization as “phat thai.” English-language menus and publications also use “pad thai” and “phad thai,” so readers may encounter several spellings for the same stir-fried noodle dish.
The spelling should not be confused with other Thai noodle dishes. Pad krapow is a basil-based stir-fry, Phat see ew is a soy-sauce noodle dish, and Pad Lao refers to a different culinary tradition. The spelling variation concerns the name, not a separate recipe.