The story takes place in an alternate reality from the rest of the Sailor Moon series, so it does not fit to the main storyline or canon. One of the main reasons it does not fit into the main storyline is because it is stated in the main series that Usagi Tsukino will only have one child (Chibiusa). However, the lead character created especially for this story is Usagi's second child, Kousagi Tsukino. The daughters of the other four Guardian Senshi (all in grade 3 with Kousagi) also are in the story, who look exactly like (and are named after) their mothers (though the Japanese spelling of the names are different).
Parallel Sailor Moon was originally released as part of the Materials Collection artbook and was reprinted in 2004 as part of the shinsouban second volume of short stories. The story was published in 1999, in honor of the Chinese year of the rabbit.
The series was published in English by Kodansha Comics USA in November 26, 2013 as part of the second volume of short stories.