Is it that different than a drummer running four different beat patterns across all four appendages? Drummers frequently describe having "four brains". I think these things seem impossible and daunting to start but I bet with practice they become pretty natural as our brain adjusts and adapts.
Speaking as a drummer: yes, it’s completely different. The movements of a drummer are part of a single coordinated and complementary whole. Carrying on two conversations at once would be more like playing two different songs simultaneously. I’ve never heard of anyone doing that.
That said, Bob Milne could actually reliably play multiple songs in his head at once - in an MRI, could report the exact moment he was at in each song at an arbitrary time - but that guy is basically an alien. More on Bob: https://radiolab.org/podcast/148670-4-track-mind/transcript.
Wow, that ability is incredible! Thank you for sharing.
I mean, as someone who's played drums from a very young age (30+ years now), I disagree with that description of how playing drums works. I went ahead and looked up that phrase, and it seems to be popular in the last couple of years, but it's the first time I've heard it. I'd honestly liken it to typing; each of your fingers are attempting to accomplish independent goals along with your other fingers to accomplish a coordinated task. In percussion, your limbs are maintaining rhythms separate from each other, but need to coordinate as a whole to express the overall phrase, rhythm, and structure of the music you're playing. When you're first learning a new style (the various latin beats are great examples), it can feel very disjunct, but as you practice more and more the whole feels very cohesive and makes sense as a chorus of beats together, not separate beats that happen to work together.