I think the term also applies to small candies in general. My dictionary lists “a small candy in a ball or disk” as the first definition with “sweetmeat” as a synonym. “Sweetmeat”, in turn, is defined as “candied fruit” as well as “candy, confection”.
The second definition for “sugarplum” is “serviceberry” (which my mother pronounces “SAR-vis-berry”) which sounds like the fruit you described, Flora.
So I think this is an example of a specific item (the candied sugar plum) becoming a generic name for any small round candy. My mother likes candied fruit, which I assume she enjoyed as a child, but the ones she made for us (which went uneaten) were not plums but orange and other citrus fruit rinds (ugh!). She never called them sugar plums, though. I’ll have to ask her if she ever had a true sugar plum.
“The inability of science to grasp Quality, as an object of enquiry, makes it impossible for science to provide a scale of values.”