Basically, tango shoes and salsa shoes are quite different in terms of soles and heel styles.
Salsa shoes usually have a soft, chrome leather sole that is flexible and moves with the foot. The chrome leather sole (a type of treated suede) is used to help you glide while dancing and turning, but still stick to the floor a bit.
The heel of a salsa shoe has its origin in Latin dance and is called a flare heel. This means that it is curved in the middle and becomes wider at the end so that you have more stability.
Tango shoes generally have a hard (less flexible) leather sole. It is not suitable for Salsa or Latin as it would be too slippery. The Tango heel is also much thinner compared to the Salsa / Latin heel and usually higher. It could also be called a pencil or stiletto heel.