Your Day is definitely a Dolma. I have a Dolma Work, and it looks like mine
The second one is often called as " monk" bag, I'm not exactly sure if that's the official name for it, though. As far as I know, "monk" is a name for the particular super soft leather used on those non-moto bags Bal did in 06, and yours seem to be Ink.
Balenciaga started changing the rivets to notched ones in the season that Dolma was made which I believe was '05 pre-spring. Some bags have the notched rivets and some have the ones like yours. I have an authentic Dolma City that has rivets like yours. I LOVE Dolma! Beautiful!