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Note: A shape layer stroke is a vector-based stroke and is applied only to shape layers. This is very different from the layer syle stroke.
You can control the settings for this stroke in the options bar for the vector tools (Shape, Pen, Path Selection, Direct Selection). This stroke is an attribute of the shape layer and will not cause the fx icon to display on the layer in the Layers panel.
A layer style stroke is a pixel-based stroke and can be applied to any layer that accepts layer styles (including shape layers). The settings for this stroke are controlled via the Layer Styles dialog.
The layer style stroke effect and the vector strokes are completely different beasts.
The layer style stroke effect is just a filter run on the pixels of your layer - it can't do dots, dashes, square corners, etc.