Hash of public key as address

[highperspective]

Is it correctly understood, that the transaction creator (A sends money to B) A, addresses the transaction to the hash of B's public key? In order for B to redeem this transaction later, he has to proof that his public key hashes to the same hash, as A addressed the value to.
And by this and the "sig", B redeems the right to the value, previously addressed to him/her.