Classes in CSS allow the same styling to be applied to multiple elements, while IDs can only be applied to individual elements. Classes are defined with a "." prefix followed by a name, then curly braces containing style rules, and are applied to elements using the "class" attribute. IDs are defined with a "#" prefix followed by a name, then curly braces containing style rules, and are applied to elements using the "id" attribute. Both classes and IDs allow for reusable styling without repeating CSS code.