A story that was published in two or more parts in a magazine. Sometimes these parts were collected and published as a book, occasionally part of a series.
For people who are generally outside the series book collecting field, the phrase “serial” might be applied when “series book” is intended.
The image below is an sample page from American Boy magazine containing a story that was later expanded and published as a volume in the Adventures in the Unknown series (Grosset & Dunlap, 1933-34) by Carl H. Claudy. The illustrations in the book were different as well.