The token is the money: the token is the IOU. The token you attached to your note was an IOU for 2 satoshis but it was not 2 satoshis in the sense of a lightning or on-chain payment. (yes, for 2sat both of those would not make much sense)

Send money offline: The sender can be offline and pay invoices to a recipient at the denominations that he is carrying tokens with him. The recipient can offline verify that the token was issued by the mint but cannot know if it was spent already without talking to the mint. Great for async tipping. Not so great for POS situations with one of the parties being offline.