I am leaning towards Fencedude's opinion, with only slight reservations.
Some facts about the Hanabira series, collected by Yi Hsieh, the author of "Listless Ink":
Yuuna and Nanami are the protagonists of games I and VI (as well as some of the light novels).
Sara and Kaede are the protagonists of games II and IV (as well as some of the light novels).
Mai and Reo are the protagonists of games III and V and the "Anata to Koibito Tsunagi" OVA (as well as some of the light novels).
All characters, including those of Hanahira, are pupils of the St. Michael’s All Girl Academy [please mention the school's Japanese name if you know it].
Cross-referencing does happen: at least Yuuna of Hanabira I makes a guest appearance in Hanabira II. (This proves the existence of a fictional "Hanabira universe".)
Yi Hsieh calls the non-hentai game "Hanahira! Side Story (SS)" and "a side story to the original series". Unfortunately I cannot tell if this is a conclusion by the blogger or based on official information from Fuguriya.