I'd say Ruby mixins
are more similar to Java interfaces
than Java class variables.
Similar to Java, Ruby does not have multiple inheritance. In both languages a class can only have a single parent class (although that parent, can have it's own parent, and so on).
Similar to how Java uses interfaces
to declare functions that all implementing classes should define, Ruby uses mixins
to enhance the functionality of a given class hierarchy.
Java instance variables are defined within the class, while Ruby mixins are like adding a new parent class in between your current class and its parent. To objects of the class, yeah mixins might seem similar to Java instance variables (in the same way that an object doesn't know the difference between what members it receives from its instantiating class and what members were inherited from parent classes).
Maybe the important distinction is that Ruby mixins are added to the inheritance hierarchy while adding Java instance members requires modifying the actual class.