If I delete messages on my iPad to free up space, will they be deleted everywhere else?

If you have enabled iCloud Messages for all of your devices, message deletion on one device will be synchronised to your other devices.

Should you choose to de so, you can disable iCloud Messages on one or more devices. You don’t mention the installed iOS/iPadOS version for your devices; to disable iCloud Messages:

iOS/iPadOS 16.x

Settings > [Your Name / AppleID] > iCloud > [Apps Using iCloud] Show All > Messages > Sync This iPad - set to OFF

iOS/iPadOS 15.x and earlier

Settings > [Your Name / AppleID] > iCloud > Messages - set to OFF

If you only wish to delete received message from your iPad - but retain the benefits of synchronising your iPhone with iCloud - you can simply disable iCloud Messages on the iPad; while the iPad will continue to send/receive messages, deletion from iPad will not be synchronised with the iPhone.

chrisbenz Said:

"If I delete messages on my iPad will they delete everywhere else? It is a bit confusing because it says my iPad storage is full but all that should be on the cloud like my other devices."

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Archive these iPhone Messages:

These are stored on your Cellular network. So, create a backup, as YES. They will be deleted everywhere. So, make an archive of these. Take screenshots of the thread, or screen record as you scroll down the thread. Arrive what is created. Learn More Here: Take a Screenshot or Screen Recording on iPhone - Apple Support