The two classes

com.sun.java.swing.border.TitledBorder
com.sun.java.swing.SwingConstants

Both define LEFT, RIGHT and CENTER. The first is used for text justification, and the second is for "alignments"

In addition, the values of these two versions of LEFT, CENTER and RIGHT are different (1, 2, 3 in the former, 2, 0, 4 in the latter).

Also, wouldn't it be more consistent if TitledBorders used "alignment" terminology just like the other swing components (AbstractButton, JTextfield...) rather than using "justification" ?

I don't care which term you use as long as it's the same.