You own the card. The token is a transferable claim on one specific slab, matched one to one with its certification number, and it exists so the card can change hands without anyone shipping it, opening it, or risking it in the post.
The card itself does not move. It stays sealed in the vault, insured, while the token travels. When you want the physical card, you redeem the token, the token is burned, and the card ships to you.
Tokenization is not live yet. The page describes exactly how it will work and what it will cost, and it will not accept a card until the terms are final.