staticInit is a static variable of class X. Therefore, when you access it, only class X is initialized. This is true even when you access it via Y.staticInit. Y.staticInit and X.staticInit are the same variable.

Only when you access the first static variables of Y (Y.staticInitRe in your first snippet), class Y is initialized, which also changes the value of X.staticInit to 1.

On the other hand, X.staticInitRe and Y.staticInitRe are different variables and X.classicInitRe and Y.classicInitRe are different variables.

The first snippet :

    System.out.println("staticInit X: "+X.staticInit); // X is initialized. All all of its 
                                                       // variables are initialized to 0
    System.out.println("staticInitRe X: "+X.staticInitRe);
    System.out.println("classicInitRe X: "+X.classicInitRe);
    System.out.println("");

    System.out.println("staticInit Y: "+Y.staticInit); // Y is not initialized yet
    System.out.println("staticInitRe Y: "+Y.staticInitRe); // Y is initialized: 
                                                           // Y.staticInitRe, 
                                                           // Y.classicInitRe and 
                                                           // X.staticInit are assigned 1
                                                           // before this String is output
    System.out.println("classicInitRe Y: "+Y.classicInitRe);
    System.out.println("");

    System.out.println("staticInit X: "+X.staticInit); // was changed to 1 by Y's
                                                       // static initializer
    System.out.println("staticInitRe X: "+X.staticInitRe); // remains 0
    System.out.println("classicInitRe X: "+X.classicInitRe); // remains 0
    System.out.println("");

    System.out.println("staticInit Y: "+Y.staticInit);
    System.out.println("staticInitRe Y: "+Y.staticInitRe);
    System.out.println("classicInitRe Y: "+Y.classicInitRe);
    System.out.println("");

The second snippet doesn't access any variables or methods of class Y, so class Y is not initialized, and X.staticInit remains 0.

JLS 12.4.1. specifies when a class is initialized:

12.4.1. When Initialization Occurs

A class or interface type T will be initialized immediately before the first occurrence of any one of the following:

• T is a class and an instance of T is created.

• A static method declared by T is invoked.

• A static field declared by T is assigned.

• A static field declared by T is used and the field is not a constant variable (§4.12.4).

• T is a top level class (§7.6) and an assert statement (§14.10) lexically nested within T (§8.1.3) is executed.

Since Y.staticInit is not declared in Y, using that field doesn't initialize class Y.