How do I sync Messenger between iPad and iPhone ?

Hello Kenny,

Thank you for your question. Deleting messages on one device will not delete the message on your other devices, but you can choose to disable iMessage or unlink your phone number.

You can disable iMessage on your iPad by going to Settings > Messages.

iPad User Guide - Messages settings

http://help.apple.com/ipad/7/#/iPad99acb5bb

Alternatively, you can unlink your phone number from your Apple ID on your iPhone if you would only like to receive messages that are sent to your Apple ID on your iPad:

Unlink a phone number

To remove a phone number from an Apple ID, sign out of FaceTime and Messages on your iPhone:

• Settings > Messages > Send & Receive. Tap your Apple ID, then tap Sign Out.
• Settings > FaceTime. Tap your Apple ID, then tap Sign Out.

This should remove your phone number from other devices using the same Apple ID with FaceTime and Messages. If the phone number is still available on other devices after you sign out of FaceTime and iMessage on the iPhone, you may need to sign out of iMessage and FaceTime on all your devices, then sign in to FaceTime and Messages again on devices you want to use.

Note: If you no longer have access to the iPhone that is using the number you want to remove, reset your Apple ID password.

You can find the full article here:

iOS and OS X: Link your phone number and Apple ID for use with FaceTime and iMessage

http://support.apple.com/kb/HT5538

Thank you for using Apple Support Communities.

Best,

Sheila M.