Two-way payments let two parties each sign compatible halves so the exchange clears in a single consensus round when the protocol and client support it. The sequence (draft, exchange of partials, final combine, and broadcast) is client-specific.
Concept
See Two-way transaction (concepts) for the network-level idea, then your SDK for the exact call order.
API-level background
Transaction (mempool) and create_transactions show the raw request shape when you are not using a high-level client.