1. I want to eat sweets.

2. I want to eat candy.

(Are both the same? What is 'sweets'?
Are sweet foods all sweets? Or sweets is just candy?)

The British usually use "sweets" the same way the Americans use "candy."

Your first sentence is correct for Britain; the second is more common for the U.S.

http://www.macmillandictionary.com/dictionary/british/sweet_23

1. "I want to eat sweets" is a statement indicating a desire to consume a type of food that is generally sweet in taste. "Sweets" is a term that encompasses a wide range of sugary, sweetened foods, including but not limited to candy. It can include desserts like cakes, cookies, and pastries, as well as other confections like chocolates and ice cream.

2. "I want to eat candy" specifically refers to a type of sweet food that is usually made with sugar or syrup, flavored, and often shaped into smaller, bite-sized pieces. Candy can come in various forms, such as hard candies, gummy candies, chocolate bars, or lollipops.

So, while sweets can include candy, it is a broader term that encompasses a wider variety of sweet foods. If you specifically want to eat candy, you are referring to a subset of sweets.