I am presently doing a course in Core Java.
I am also working in J2EE.
I have seen that core java technologies are mostly related to J2SE
i.e the standard edition. These are not used very much in web architecture.
Advanced Java basically deals with the web development like servlets, EJB, etc
I am working in J2EE and most of the technologies I am using fall under the Advanced topics.
So my perspective is core Java is more like non-web based applications
and Advanced Java is for web based applications.