Precisely defined concepts matter more in board games than in life, and more in Dominion than in most board games. This doesn't necessarily mean that the words always have to be consistent (e.g. "when this is your first buy" is a variant of "when you buy"), although it helps.
The point of saying that Animal Fair has an alternate cost is that this would mean that you can choose it without breaking the rule that you can only choose a card "costing as much $ as you have or less". It would be a cost that you don't pay, rather you do something else instead. We have precedent for this, with Debt. Debt comes with a rule that you don't pay the Debt cost, you take tokens instead. So Animal Fair would have the cost "$7; or trash an Action card from your hand". Since the basic buying rule is that you pay from what "you have" to cover the cost, we actually need to define that the "trash a card" part of the cost is like Debt, that you don't pay it.* (The card says that you trash a card instead of paying its cost.) This has to be an implicit extra rule. Unlike Debt this cost is something you have to "have", so we need to also say that having an Action card in your hand means you "have" enough to cover that cost.
But if that is really the cost (at all times), then Wayfarer would get that cost (just like with Debt), to just state the simplest example. So unless the cost varies (which is what I said was contradicted by several things), we need more implicit extra rules, like hhelibebcnofnena says. We need to redefine what "cost" means! But only in certain situations - only when cards mention cost, not when the rules for buying mention cost, because then we would be back to square one! So on all cards, "cost" now means numerical cost - including Animal Fair itself - while in the rules it would vary: sometimes "cost" means "cost", sometimes it means "numerical cost". I don't think this is a good way to view this.
I really don't think Animal Fair is supposed to redefine what "cost" means in the game (certainly not in an inconsistent way), rather it's supposed to be an exception to the buying rule, allowing itself to be chosen even if you don't have the cost, as long as you have an Action card to trash.
Also, it's just very unintuitive that the card says to trash a card instead of paying its cost if trashing a card is also its cost.
*I see that some places in the rules, and Donald's writings, say that trashing a card is a way to pay for Animal Fair. Obviously this is not the normal definition of "pay" used anywhere else, which means to deduct the cost from your pool of coins (or potions). (Debt does not say that taking Debt tokens is a way of paying.) It's probably best viewed as a shorthand for doing something else instead of paying, understandable used in the context of buying Animal Fair.