1. If you have a 24V load, you send it 24V from an output card.
Example: If you have a 24V coil in your relay, you send it 24V when you want it to close it's NO contacts (or open it's NC contacts).
2. If you have a 120V load, you send it 120V from an output card.
Example: If you have a 120V coil in your relay, you send it 120V when you want it to close it's NO contacts (or open it's NC contacts).
3. If you have a 120V load but only 24V available at your output card, you install a relay with a 24V coil to the output card. Then you wire your 120V load through the relay.
4. If you have a 24V load but only 120V available at your output card, you install a relay with a 120V coil to the output card. Then you wire your 24V load through the relay.
If you send 24V to a 120V load, good luck getting the desired results.
If you send 120V to a 24V load, good luck getting a new job.