The two tills disagree about a posted order
Lightspeed records the sale as fulfilled. Clover has nowhere to record anything.
Ship an order that came from Lightspeed and we set it fulfilled, which is as far as Lightspeed can go: it stores no carrier and no tracking number against a sale. So the sale stops sitting in the outstanding list, and the one piece of information a waiting customer wants is not on the record. That is a limit of Lightspeed rather than a step we have skipped.
Clover does not go even that far. It has no field for a tracking number at all, so nothing about the parcel reaches the Clover record. Between the two, Lightspeed gives you half the handshake and Clover none of it, and the number itself stays in QuickSync either way. That is where to look, and where to point anyone on your team who asks.
None of this is unfinished work waiting on us, and a page telling you tracking flows both ways would be wrong in the way you only discover with a customer on the phone. If somebody reads shipping detail off a till as part of their day, this is the pair to plan that around before parcels start going out rather than after.