I am still working on this, but as far as I can tell messages sent to my iPhone telephone number will NOT sync with my iPad. But if a message is sent to my email address it will show up in both places.
I guess that this makes sense but it flys in the face of being able to easily start texting on my phone and then just picking up my iPad when I get home and being able to continue the "conversation" on either device. Most people when they send a text message will do it to the phone number because that's the way we have been trained up to this point to send text's. But once I get a thread running in either place, no matter how it got it started, I seem to be able to respond on either device and keep going.
I guess we will need to learn to send text's to email addresses if we want to be able to keep a text thread in sync on all of our devices.