Does the phase relationship matter? For instance, with a mass on a spring, position and velocity are 90 degrees out of phase. But does it matter to say which leads the other? After all, that seems like a matter of initial conditions that goes away after an oscillation.

For the AC circuit it seems a bit more important to say whether voltage leads or lags current, since it's not always that clean 90 degrees difference in phase. But does this have any physical meaning, whether it leads or lags an by how much?

I know that if we think of the voltage across each element in an RLC circuit as a vector rotating around the origin, then we can take the vector sum of those 3 vectors and compare it to the voltage across the resistor to see whether it leads or lags. But does that matter?