How to sync ipad and iphone

If you have an iPhone - and both iPad and iPhone are signed-in to iCloud with the same AppleID - to send SMS/MMS messages (green bubbles) from your iPad you must explicitly enable Text Message Forwarding for your iPad on your iPhone...

On your iPhone:

Settings > Messages > Text Message Forwarding - set to ON - and explicitly enable your iPad from the list of devices.

Also ensure that Messages in iCloud is enabled on both your iPhone and iPad:

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

Are Messages set to sync? Change which apps sync and store data with iCloud - Apple Support