A shape is not a style

You can save a shape as a custom shape, or as a custom brush.
To save as a shape:
In the Paths palette, select a path or a vector mask. Edit > Define Custom Shape. Name the thing when asked. It will appear in the current custom shape pop-up. You can, of course, create a new shape palette in the Preset Manager (Edit > Preset Manager) so you can organize your shapes.
To save as a custom brush:
First, rasterize your shape by Cntrl/right-clicking on its layer and choosing Rasterize.
Then, select the rectangular marquee and select your shape with it (make sure feather is set to 0). Black or greys on solid white work best. Edit > Define Brush and name it. Again, you can organize your custom brushes through the Preset Manager.