Does the payload capacity of a rocket include the satellite and the adaptator or is it just the satellite ?
Payload is normal taken to mean amount of mass the rocket can lift in default form, so any one off adapters or supporting hardware will need to be subtracted from that number.
This can result in some ambiguity in useful lift, where some systems can provide more services like cooling or power to the lifted satellite, or reduce the vibration/G-loads and therefore needed supporting structure. allowing a customer to use more of the payload for the satellite itself.
It is also worth noting that payloads are normally to specific orbits, so comparison can only be done where both target orbits are known and the same.