These are extremely similar ideas, with broad, fuzzy definitions, which make it tricky to answer with certainty.
Serious Games (coined in 2002 by Woodrow Wilson Center for International Scholars): is a game designed for a primary purpose other than pure entertainment.
Gamification (origin uncertain, became popular in 2010): applying game design thinking to non-game applications to make them more fun and engaging. (ref 2)
Both terms have been used for a whole variety of things, and, broadly speaking, are really just different terms for leveraging game techniques in non-traditional ways.
In practice, the two terms tend to be used in different contexts, in slightly different ways, for slightly different purposes.But these differences are not strictly adhered to.
A key difference in the definitions is that a Serious Game “is a game” and Gamification is applying “game design thinking”. This supports my understanding that serious games are usually complete games, whereas a gamification example is less likely to look like a game, and may just have a few game-like elements (think on eBay or Stack Exchange or the admin side of Wikipedia).
Serious Games arose from an academic organization with policy goals, and they tended to emphasize positive social outcomes; whereas gamification has tended to be used in business and marketing as a tool for improving profits.