The Menagerie rules say, exact quote: "Enchantress from Empires also changes what an Action card does when played." "Also", in this context, means in addition to Ways—so this sentence presupposes that what Ways do is, in fact, changing what an Action card does when played.
And yet, neither Enchantress nor Ways entail shape-shifting, for the reason you state. So, "changing what a card does when played" isn't shape-shifting. The instructions on the card don't change; just what the card does when played changes. Ordinarily when you play a card, what the card does is what is detailed in its instructions; when you use a Way or are under the influence of Enchantress what the card does is something else.
I take that as short-hand for "makes you change what instructions you follow when you play the card", which we know is exactly what happens with both Enchantress and Ways. As I'm sure you know, the rules in the rulebooks use shorthand that is understandable for casual players and also usually accurate in the majority of situations, but not always technically accurate in all situations.
If what literally happens is that Ways change what a card does, what does that mean? How is "what a card does" different from the card's instructions? How are "the card's instructions" defined if not "what the card does when played"? This is what I asked a couple of posts up.
Yes, I agree, "changes what a card does" does mean "makes you change what instructions you follow when you play the card". So, to answer your question, how is "what a card does" different from the card's instructions?, well, as a first draft here, "what a card does" is
the instructions you follow when you play the card, which may or may not be
the instructions actually printed on the card (i.e., the card's instructions).
Or actually, let me revise that a bit: what the card does isn't quite
the instructions you follow when you play the card, but perhaps it's actually
the sequence of game moves players take as a result of following instructions upon playing a card. For instance, Steward's
instructions are:
Choose one: +2 Cards; or +$2; or trash 2 cards from your hand.
And if I play a Steward and choose +$2,
what Steward did was (1) caused me to make a choice and (2) gave me $2.
If I play Harbor Village and then Steward, choosing +$2, I get +$1 from Harbor Village because giving me coin is something the Steward did. If I play Harbor Village and then Steward, choosing +Cards, I get no coin from Harbor Village because Steward didn't give me any coin (even though +$2 is apparently part of Steward's instructions). And if I play Harbor Village and then Smithy, choosing to play Smithy according to the Way of the Sheep, Harbor Village gives me +$1 because giving me coin is something the Smithy did.