These terms don't mean anything certain in technology and Java-related fields. Well, "core" is general term typical for engineering, with intuitively apparent meaning, something which does not have and does not imply strict definition. "Advanced" is even wider notion, with even more obvious meaning. If you heard these "terms" anywhere, it could mean some basic classification of skills of type of activity, which is not mandatory or instructive to anyone. In simple words, just "blah-blah-blah". Therefore, the question makes no sense; and you don't need to be concerned with those words.
To learn about Java, first please see:
http://en.wikipedia.org/wiki/Java_%28programming_language%29[
^],
http://en.wikipedia.org/wiki/Java_%28software_platform%29[
^].
—SA
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