Punch is typically referring to a waveform with high dynamic range - the opposite of compressed. Warm usually indicates a sound with rolled off highs and boosted midrange.
Interestingly, in addition to being a bassist, I'm also an electronics freak. I've studied every amp schematic that I can lay my hands on, have built my own gear, and read a lot of online commentary on the subject.
In my observation, a fair generalization is that for every term describing tone quality, there are equal and opposite definitions and explanations.