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For me, a serial is a single book broken up in multiple chunks (I have very fond memories of reading quite a few books in Analog and other SF&F magazines published that way) whereas a series is a collection of related books.
As an example, Lois McMaster Bujold's Falling Free was serialized in Analog magazine (Dec. 1987 to Feb. 1988) while it is part of her Vorkosigan Saga series since it shares the same fictional universe and the quaddies made appearances in other Vorkosigan Saga stories.
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