Do Nike shoes run really small?

I’m in need of a good walking/running shoe so I was browsing the Nike website and realized that, according to their website, I’d wear a size 9 in women’s. It shocked me because I’m typically a 7.5 to 8, depending, but definitely never a 9 – because that would just be way too big, usually.

I know my best bet is to actually try some on, but in this case, that’s not going to happen. So, if you’re pretty familiar with Nike shoes and sizing, do they really run that small?