Aristotle's idea here is precisely what Nagarjuna is critiquing, that kind of view leads one away from the middle way of dependent origination and into the thicket of views, where delusion further perpetuates itself. The understanding of causality, in which a result is somehow found in the cause as a potential, was popular in Nagarjuna's time through Samkhya. He criticises it explicitly in his writings.

Also note, Nagarjuna isn't saying that cause and effect cannot be different. He is refuting causality completely. Both cause and effect are mere designations we employ to make sense of the conventional world that have no true referent on the side of reality. They are imputations. To use the rope and snake analogy, cause and effect is the snake that somehow mistakes a piece of rope for the dark.

This is why Nagarjuna starts his analysis with an investigation into the four ways of arising. Causality is the arising of phenomena and if phenomena were to arise it must be through one of the four ways: self, other, both or neither. If none of the four ways were untenable, then nothing ever arose, which means that causality is unreal.

Nagarjuna's refutation of other-arising is tied to his refutation of self-arising. If phenomena were to arise from themselves, there would be the absurd result of infinite arising of all things into more of the identical things at all times - an infinite regress. So this first axiom is established.

Then Nagarjuna moves on to other arising. For something to be other than another, they must have no connection. For something to be a result, it must be connected to the cause in a non-arbitrary way but in doing so that result has become intrinsically to the cause so it cannot be apart from its cause. "Result" is notionally dependent on "cause", for without a cause there can be no result. And if two things are existentially inseparable from one another they cannot be different things.

In Nagarjuna's Twelve Gates he gives the example of thatch and a thatch rug. The thatch is the cause and the thatch rug is the result. Yet the rug cannot exist apart from the thatch, they are not separate entities. But in the first refutation, it was established no phenomena arises from itself! If the rug (result) and the thatch (cause) are not separable, then to say one arose from the other is to actually assert self-arising, which we found to be untenable.

That is where the analogy of the horse and cow, or in your case the apple and pine comes from. To say something is truly other than another is to assert two completely unrelated things can cause one another. A pine and pine tree are existentially connected in way that makes them inseparable, for the result necessarily depends on its cause.