All sheep that have wool (there are also hair sheep that do not) are dual purpose, but some breeds have more desirable wool than others, and different wool qualities. Merino and merino-type sheep have long, fine wool that is in demand as wool. Breeds like Suffolk and Hampshires have coarser wool that is less desirable for making clothing, but also stronger fibers. The Navajo-Churro breed has long, coarse wool that is sturdy and ideal for rugs and blankets.
Different breeds do get targeted to different markets. So for example, we have Suffolk/Hampshire black faced crosses, which are colloquially known as “club lambs” because these are the sheep that are raised for 4H and FFA shows and sold as market lambs. As you might guess, ours are the result of a now-adult child’s 4H project.
Sheep vary quite a bit in size. Some are the size of small ponies and some are the size of medium dogs.
Merino-type breeders especially in Australia and New Zealand are constantly upgrading their flocks to improve meat production, since selling both is a better economic plan. In the US people tend to choose sheep for their meat production qualities, because the market for wool is weak.
One of my favorite books on this topic, “The Fleece and Fiber Sourcebook” by Robson & Ekarius, lists around 100 breeds of sheep and the various characteristics of their fiber.