Basketball shoes, really good ones like Nike and Reebok, will have added shock absorption, breathable fabric and anti skidding, anti scratching marking at the bottom of the shoes.
Basketball shoes are designed in a way to support your ankles, so when you jump all over again you will not get hurt. Other sport shoes are most of the times designed for running jogging or gym. Nowadays sport shoes are also used as every day shoes, basketball shoes cannot be wear as casual shoes.
Basketball shoes usually give your ankles more support and are designed for the indoors. Most other sports' shoes are designed for outside and sometimes have "cleats" on them.