Though I think there's a difference between having 'the internet' stored in a preindexed form against which you can perform direct exhaustive lookups, and having instead a set of weights that were produced by having once been exposed to a large amount of the data on the internet.
But you're right to point out that the difference between them is not actually that great, and both of them are really a form of 'recall'.
Isn't Google index much *much* larger though? There's a large amount of compression going on here (of course, not to say it hasn't probably memorized certain texts obviously [both important/factual snippets and less important bits as well]).
That does seem to be the huge difference here which yields the wonderful features of this system.