Hi Theyarealivin!
I used the application "iMazing"...excellent program (stupid name). The cost is $30 - 45 depending on which license you purchase. It is free to download to test out, but to do much more than test, you would need to purchase the application. The application runs on the Mac.
Someone else on these forums mentioned this as an excellent tool for useable/dependable backups vs. iTunes.
It does backups and software upgrades and more.
So I wanted to copy my messages/SMS from my old iPhone 6SPlus to my new iPhone X. But first I wanted to set the X up as a new phone. So I did that, got everything configured, and then went about the process to transfer ONLY my SMS/texts from the oldie to the newbie.
It did work beautifully.
Note: I did not transfer my photos from my photo library - I backed those up to my iMac and didn't want them on the new device (@20GB photos); they're better saved on 2 different external hard drives and in an editable/backup.
If you would like the instructions I used, just let me know. I don't want to make this post too long.