Issuer shares with Subject the authorization to the Resource. When Bob deposits the payment from Alice, he knows he has excluded anyone else from using that money. In the capability case, if Alice drops the capability after passing it to Bob, Bob happens to have exclusive access to Carol, but this isn't an exclusive right since Bob is unable to know that he is the only one who has it. In the real world, information is sharable and physical objects are exclusive. A capability designates a specific object.
Authorization can be for specific objects, or for some number of units.
Money is fungible , since we care only about quantity, not individual bills. A capability is opaque , since from the capability alone all you can determine is what the designated object alleges about itself. An authorization can be read as well as used. Reading it may suffice to assay what value it would provide. Bob can reliably assay the amount in an alleged purse only by transferring into a purse he trusts.