The casual footwear with a Y-shaped strap passing between the big toe and second toe is a flip-flop.
Flip-flops have a flat sole held to the foot by a thong-style strap. The strap branches toward both sides of the foot and joins between the first and second toes, creating the characteristic Y shape. They are usually lightweight and worn as informal warm-weather footwear.
Thong sandals have ancient roots: examples and depictions appear in several cultures, including ancient Egypt, Greece, Rome, India, China, and Japan. The modern American flip-flop was influenced by Japanese zōri sandals after World War II and became strongly associated with beaches and summer clothing in the 1950s and 1960s.
A common mix-up is treating every open sandal as a flip-flop. Slides, espadrilles, and strappy sandals lack the defining between-the-toes thong. In Australia and some other places, the same footwear is commonly called a “thong,” though that word has a different meaning in American English.