Well, both seem to matter, but it seems the knight matters more.
For example, we have examples of squires being knighted for winning squire’s tourneys (some of which are rigged), which seems a bit low prestige compared to, say, saving a lord from an outlaw, or unhorsing a prince and the Lord Commander of the Kingsguard. OTOH, if you’re knighted by Arthur Dayne or Gerold the Bull or Ser Barristan the Bold, that name carries.
So yeah, I think your analogy is apt. Apt, I say!