**Personal opinion alert**
sequel - stand-alone story that has in common with the previous stand-alone a more-encompasing, overarching plot or story arc.
series - stand-alone stories that use the same characters, but put in different situations - typically without an overarching plot, but held with some other common bond (like occupation or activity of the MC, for example a series of stories with the same professional or amateur sleuth). Characterization is carried through, and the history of past stories may be important.
From the description here, I don't think picking off characters from a subplot and writing a full story about them makes the story either of the above. It's just picking off familiar characters and writing a unique story that has some relationship with the first story. Of course, it depends on how close the new story follows the subplot of the original story. Is it an outgrowth? If it is an elaboration, it couldn't be a sequel if it was either happening simultaneously with the original story, or before it (if the elaboration of the subplot went back in time relative to the original story). In other words, the temporal relationship between the two stories is important.
For this to be considered a series, there should be some common MCs, and I don't see where secondary characters fit that bill. My current WIP uses characters from Agnes Hahn and Imola, but I do not consider it either a sequel or part of a series because it is a totally unrelated story, even though there are references to the original two stories.