I've been told in the past that Photoshop shapes aren't vectors. The context was that vectors can be resized without loss of resolution.
Do Photoshop shapes (if saved as psd or psb files) lose resolution when resized like rasterized layers?
Yes, Adobe Photoshop treat its custom shapes as vectors, but you can also draw vectors with
Pen Tool. And after saving as
psd Photoshop will retain its properties.
If you save the document as a PDF or EPS, it should retain the shapes just fine. I'm not sure exactly how PS interprets shapes but in some cases they do hold up just like a vector.
Yes, shapes are vectors and no, you will not degrade quality of shape if you will resize it. But, in the same time do remember, that shape is rasterised afterwards in the resolution of your canvas. Take that in mind, when saving lo-res psd and then wondering, why it's not printing in hi-res.