One major difference between the Hindustani and Carnatic traditions can be seen in their treatment of improvisation. In his book A Southern Music, Carnatic vocalist T.M. Krishna explains improvisation in the context of Carnatic music:
The [Sanskrit] word manodharma has two components to it: mano, meaning ‘one’s own will’, and dharma, which refers to a certain righteousness in the path… Improvisational music is what is referred to as manodharma sangita, or the music that issues out of the individual musician’s very own and personal musical sensibility.
In both systems of Indian classical music, improvisation within a raga (melodic scale) is seen as the highest level of musical skill; in no musician is qualified to perform if they are not proficient in improvisation (which is why I have a while to go until I give a concert, lol), and indeed improvisation plays a central role in Indian classical performances.
In Hindustani performances, improvisation makes up the vast majority of the concert; there may be a few compositions with defined lyrics and melodies that are performed, but the rest of the concert is raga-based improvisation. In a typical Hindustani concert, the performer will say, “I will now play/sing Raga ___”, (or they might not say anything) and they will begin a certain type of improvisation in that raga. They will then move on to another raga or two, and then end the concert with some short compositions.
In contrast, Carnatic performances are typically driven by compositions, not freeform improvisation. Instead of just announcing the name of a raga, the artist would typically say, “I will now perform the song ____ in ____ raga, set to ____ talam (rhythm), dedicated to Lord/Goddess _____ and composed by _____.” They would then begin by improvising in the raga in which the composition is set, and then they would sing the composition itself, which would have defined lyrics set to a specific rhythmic cycle. Within Carnatic compositions, there is plenty of scope for improvisation, but the artist cannot deviate from the lyrics of the composition.
This reliance on compositions with set lyrics presents listeners and performers of Carnatic music with this question: