Core Java" is Sun's term, used to refer to Java SE, the standard edition and a set of related technologies, like the Java VM, CORBA, et cetera. This is mostly to differentiate from, say, Java ME or Java EE. Also note that they're talking about a set of libraries rather than the programming language.
"Core Java" is Oracle's definition and refers to subset of Java SE technologies.
This actually is not related to Java language itself but rather to set of some 'basic' packages. As a result it affects development approaches.
Currently Java Core is defined as a following set:
• HotSpot VM
• Java Naming and Directory Interface (JNDI)
• Application monitoring and management
• Tools API