Pocketed coil mattresses have several coils individually encased in fabric. Since each coil functions independently and flexes only when pressure is placed directly on it, pocket coils are very responsive to the sleeper's body. And because coils are not physically attached to one another, they excel at controlling motion transfer.
Wire-tired coils have several rows of singular wires molded into the shapes of a circle. This structure provides the mattress a more stable core and makes it very durable. However, they may be noisier and not as great with controlling motion transfer as pocketed coils. This may be something to consider if you consistently share your bed with a partner, especially with one that tosses and turns through the night!