No, they are not. Shoes with a wide toe box are wider up at the top where the toes are, giving your toes more room. They are usually sized as a "B" (women) or "D" (men) width, which are standard, medium width shoes. But the last (the shape of the shoe) allows for more room at the toes. The midfoot and heel are medium width.
Wide width shoes offer more room in the entire shoe, not just at the top with the toes.