I don't know about the behavior of the horizontal slider bar as I would have to find where I put my old Apple mouse with the rollerball.
The vertical slider bar on the right side of a window will appear momentarily when you use the scroll wheel on your mouse but disappears as soon as you stop moving the wheel. A second slider bar would appear at the bottom of the window when the horizontal width of the window was less than the horizontal width of the content to be displayed. The Finder window in all previous versions of OS X displayed a slider bar on the right edge of the window when the vertical height of the full list of files in the directory exceeded the vertical height of the current window. I've discovered that the 'slider bars' that should be displayed when there is more content than can be displayed in a window aren't displayed or only appear momentarily.
