I’m not sure about the grey, because it looks like it is lined with sherpa, but with the black and blue their idea of lining means it has a lined hood. The body and sleeves of the sweatshirt are not lined.
Ordered same or similar in Jan 2018 and revived women’s version. Woot customer service was A#1 in handling my complaint.
These are men’s with a modern fit. This company puts zippers on the right side but that doesn’t mean it’s a women’s hoodie.