This is a good question as there are both similarities and differences. The main difference is the way to earn coins and FC. Whenever you are working for someone on their farm, for example, harvesting for them, you will gain coins. You can earn FC for free when you level up.
The FC, as mentioned, is used mainly for luxury items on the game. For example, decorations, buildings, or other "high-end" objects like the bigger tools can be purchased with FC.