There are several currencies in the game:
The main currency in the game
They can be obtained by completing Deliveries, please check this link to learn more.
It is just another way to say "Hi" to your friends. You can send and receive these coins by claiming the daily gifts from your Neighbors.
Doubloons are being granted as you progress through the archipelago islands. You can also find those coins in the chests during your journey:
Stamps can be found in the chests during your adventures through the special events:
All of those coins can be used for purchasing various decorations for your island. Open your Shop and choose the corresponding tab: