They were classifiable only among three classes of animals: birds, mammals, and reptiles. No other animal types, for example, fishes, insects, crustaceans, etc. have ever had confirmed members of the talking beast category.
The name "talking beast" comes from their ability to use sophisticated verbal communication, for most, including actual human language. Dumb beasts behaved almost entirely like all the non-sentient animals of Earth while talking beasts, on the other hand, were inherently born with an ability to develop rationality and higher-brain decision-making skills. They are also to not to be confused with supernatural beasts, many of whose sapience/sentience is disputed. See a list of types at "beast".