There are three types of currency available.

Coins
Regular currency that is used to purchase decorations, plant food, travelling to islands, etc. Obtained by completing quests and from the animal's houses on your main island.

Crystals
Premium currency used to many things, but most importantly to to progress the game by completing essential tasks. Obtained by completing certain quests or in treasure boxes exposed when you clear vegetation.

Leaves
Spent to expand territory and complete missions. Obtained by completing quests or cleareing out trees or grass.