P.S., I don't have Hayek here in the house, but I suspect he has more of the traditional modern view of what analogy means. But I suspect that analogy can be much deeper and truer than what we think it was.
Actually, McInerny argues that when Thomas Cardinal Cajetan, the first great Thomist interpeter, explained what Aquinas meant by analogy, he got it wrong, and for that reason it tended to be misunderstood from that point on. Quite a large claim to make, but I think McInerny makes a convincing case, and it's his third book or so on Aquinas.
As McInerny puts it, with his detective-story style interrupting his philosophical style, “[E]tiam Homerus dormitat and when Cajetan nodded, his head hit the table” (p. ix). That's why I would recommend his book, because I think he rescues analogy from its weaker senses.
Yes, there are kinds. Can you share?