Are shapes in Photoshop vectors?

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?

Answer

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.