The distinction being made is that you can have effects that are physically unobservable.
Wavefunction collapse is a physical change in state of the wavefunction. The wavefunctions before and after collapse are distinct states. This change of state must propagate through space, somehow. And because of Bell's inequalities being experimentally violated, we know it must do so faster than light, and therefore (to some moving observers) backwards in time.
However, the change of state involved in wavefunction collapse is not locally observable. We can only detect it by looking at the correlations between the outcomes of the distant experiments, which we can only do when those results are brought home, at light-speed or slower. The change happens, but we cannot see it, so it cannot be used for communication. It is not a 'signal' in the sense of something that can be used for communication. Wavefunction collapse is a propagating change in a part of the universe we cannot see directly at the time it happens. We can only see the effect later when we know what happened at the other end.
It's not a good explanation, because the Copenhagen interpretation doesn't say anything about what physically causes collapse, by what mechanism, or how the change propagates through relativistic spacetime. It just asserts that the state jumps to one of the measurement eigenstates at random with a specified probability distribution. Because we can't observe it locally, we cannot do any experiment to measure the speed of propagation. It's not defined by theory, it's not determinable by experiment, it is a mystery.
You might gain some additional insight from considering how one of the no-collapse interpretations handles the issue. The 'Many Worlds' interpretations says that when one quantum system observes another, they interact, and the observer system transitions to a superposition of mutually orthogonal (and hence mutually invisible) states, in each of which the observer sees exactly one outcome. To the observer, it looks like all the other possibilities vanish and only one is left. But 'Many Worlds' say's they're still out there, we just can't see them. Then when the reports of the experiments are returned back to base, each sub-state of each observer can only perceive the sub-states of the other observer that are consistent. The quantum information is still there, and quantum interference between observers gives rise to the correlations.
Note: the 'Many Worlds' interpretation does not say that the universe splits. That would re-introduce the same problem when we ask what the mechanism for spawning universes is, and how fast does the 'rip' propagate through spacetime. It says that from an observer's point of view it is as if the universe split, because the alternative outcome is still there but inaccessible. The alternatives are in superposition, the same way an electron in a superposition of states is. We're just using plain ordinary unitary-evolution quantum mechanics, with no additions. All causal effects propagate at the speed of light or slower.
No quantum system can observe or physically interact with any of its orthogonally superposed alternatives. (You can only deduce that they're there because of quantum interference affecting the probabilities of outcomes. An electron passing through one slit does not see itself passing through the other simultaneously - the electron's wavefunction does not repel itself electrostatically.) Since we can never see them, we cannot be truly sure that they're still there. And from the point of view of the Many Worlds interpretation, wavefunction collapse is simply the belief that these alternative components really do vanish.
Since the Many Worlds interpretation offers a fully local explanation, where nothing has to propagate, and makes exactly the same predictions about observations as the Copenhagen interpretation, you cannot use quantum physics to communicate faster than light. Whether or not you believe it is true, the fact that such an interpretation exists logically implies that such communication must be impossible. Wavefunction collapse, if it happens, must propagate faster than light and hence backwards in time, but since the alternatives cannot be observed to be missing faster-than-light or backwards-in-time, it isn't a problem.
The interpretations are not experimentally distinguishable, so it is not a question of science. We can only choose between them based on aesthetics and practicality. Copenhagen is much easier to calculate with. And it's a moot point whether you prefer the seriously weird forever-unobservable, unexplained faster-than-light, backwards-in-time, non-linear, non-deterministic mechanisms, or zillions of forever-unobservable alternative 'worlds' in superposition with us where all the other outcomes of random quantum observations actually happened. Either way, the universe is very strange.
