You might say this is semantics but it’s been a useful distinction because every conversation around Ark I’ve had from people who thought of it as a payment pool led to the misconception that: - There is a single global state UTXO - Participating users must sign off on state updates

Thanks for your answer! I'll have to think about that. I've been using joinpool/coinpool/payment pool interchangeably for any trustless UTXO sharing (with a carve out for channel factories since that idea became popular before coinpools even though it's slso UTXO sharing). However, we do have an increasing number of timeout tree protocols (mostly sketches, I think Ark is the only implemented one) that have roughly similar properties to what you mention. Since all timeout trees are coinpools or channel factories, it may be sufficient to describe Ark as a "timeout tree protocol".