Bird-speaking is a type of animal-speaking.
Birds generally speak the same language, though dialects may differ greatly. If a person gifted with animal-speaking watches and listens closely, they may discern the tiny differences in the sounds and movements birds make and imitate them, eventually puzzling out their meanings.
Communicating fluently in the birds' tongue takes much practice, as with any spoken language. For example, Ani spent many weeks learning the goose dialect (even though she already knew swan) partially because geese are noisier and use much more body movement in their language.