This is called Granger-causality (and work on it led to a Nobel prize, so it's important and useful)... it's stronger than just correlation, and way easier to determine than true causation, but it's possible that z causes both x and y, and z's effect on x is just more delayed than its effect on y.
But it at least rules out x causing y, which is something.
> but it's possible that z causes both x and y, and z's effect on x is just more delayed than its effect on y.
This is in fact the case with the barometer falling before a storm. Both the falling barometer and the subsequent rain and wind of a storm are consequences of an uneven distribution of heat and moisture in the atmosphere approaching equilibrium under the constraints of Earth's gravity and Coriolis force.
But it at least rules out x causing y, which is something.