The discussion centers on the constancy of the speed of sound and light, highlighting that while the speed of sound is consistent within a specific medium and influenced by temperature, it is not invariant like the speed of light, which remains constant for all observers regardless of their motion. The theory of relativity is necessary to explain the invariance of light speed, while sound's speed varies based on the observer's motion relative to the medium. The Michelson-Morley experiment is referenced to illustrate that if light behaved like sound, it would have shown a difference in speed based on the Earth's movement through a hypothetical medium, which it did not. The conversation also touches on the implications of temperature on sound speed and the nature of mediums in relation to light and sound. Overall, the key distinction is that sound's speed is dependent on the observer's frame of reference, while light's speed is not.