iCloud Sync
Messages and certain settings — such as muted conversations — sync through iCloud. Any device signed into the same iCloud account will stay in sync. See Notifications for alert settings.
You might go off-grid with your iPhone and operate radio-only. When you return to Wi‑Fi or cellular coverage, both outgoing and incoming messages sync automatically. Opening the app on your iPad will show the same conversation history so you can continue where you left off.