Differences:

1. Enums extend java.lang.Enum and gain all of its nice features
   1. Automatic singleton behaviour through correct serialization
   2. Automatic human-readable .toString method on enum values without the need to duplicate your enum names
   3. .name and .ordinal special-purpose methods
   4. Usable in high-performance bitset-based EnumSet and EnumMap classes
2. Enums are treated by the language specially:
   1. Enums use a special syntax which simplifies instance creation without writing dozens of public static final fields
   2. Enums can be used in switchstatements
   3. Enums cannot be instantiated outside the enumeration list except by using reflection
   4. Enums cannot be extended outside the enumeration list
3. Java automatically compiles extra stuff into enums:
   1. public static (Enum)[] values();
   2. public static (Enum) valueOf(java.lang.String);
   3. private static final (Enum)[] $VALUES; (values() returns a clone of this)

Most of these can be emulated with a suitably designed class, but Enum just makes it really easy to create a class with this set of particularly desirable properties.