One of the customer reviews for the other book explains it. I've cut & pasted here:
Right away, buyers should know that Cialdini has produced a less-expensive version of this book. "Influence: Science and Practice" is designed as a textbook for classroom instruction. So, it has things like chapter summaries and questions that can be assigned as homework. However, the other book "Influence: the psychology of persuasion," is designed for a more general audience. The content is basically the same, but it omits the classroom-oriented layout. It's also cheaper. If you are a student who is buying textbooks online, this is probably what you (or rather, your professors) want. If not, get the other one.
I was also confused by the choice between the two books and contacted someone at the Influence at Work organization. He replied, "Although both books are based on Dr. Cialdini's years of research into the Six Principles of Influence, Influence: The Psychology of Persuasion is an older edition. There are more updated references, more recent examples and more current stores in Influence: Science & Practice. Generally, Influence: Science and Practice is a more complete discussion of the topic. We do not recommend purchasing both books."