They both look Southwest. The top black one could be early Casa Grandes Ramos blackware. The "vase" is unusual in form, but does appear to have pueblo characterization.
i was just looking at a site with Anasazi ceramics...i believe the small piece is a mug, missing the handle and some of the top...it is aful small..so maybe a childs...i have found several mugs/pieces, over the years, larger though/