Padding refers to space inside of the component, whereas Margins refer to space outside/around the component. Thus, you might have more luck changing the margins than the padding.
However, keep in mind that the position of a node is also quite affected by the Parent node that it's in. For example, if it's in a VBox or HBox, then the Alignment property of that box also affects whether the things inside of the box are centered, or aligned left/right, etc.
And naturally different layouts (BorderPane, AnchorPane, GridPane, etc.) may have different configurations/options as well.