Identifying type of decks in the Dashboard
In your Dashboard, the default deck you have a Private Deck. This would have no label on it.
Decks that you have shared with link will be labelled with a 'People' icon.
Decks that you have shared to the Deck Gallery and made Public will be labelled with a 'Globe' icon.
There is only 1 deck at any one time, so if the deck is set to Public, your modifications will be seen publicly as well. If your deck is deleted, it will be removed from the entire Deck.Toys database even if you had shared it to the Deck Gallery before.
Learn how to change the share settings here.