When to use translate and when relocate - What is the difference between translate and layout coordinates?

layout coordinates are used by Layout Managers like StackPane or VBox to control their children location. Group (and Pane) leaves children layout to developer thus there is no difference from translate functionality.

So generally you should only change translate coordinates for fine location tuning and leave layout to layout managers (actually you can't change layoutX, layoutY for nodes inside non Group/Pane layout managers)

As an example try to run next code and resize window to see how StackPane recalculates layoutBounds

public void start(Stage primaryStage) throws Exception {
    StackPane root = new StackPane();
    Rectangle rect = new Rectangle(100, 50, Color.BLUE);
    root.getChildren().add(rect);
    Scene scene  = new Scene(root, 300, 300, Color.ALICEBLUE);

    rect.layoutXProperty().addListener( (e) -> {
        System.out.println(rect.getLayoutX() + ":" + rect.getLayoutY());
            });

    primaryStage.setScene(scene);
    primaryStage.show();

}