An abstract gives the most important information (in a readable way) from a document/story/technical dissertation. It may not be readable as a "full story".
A precis reduces the size of a document/story/technical dissertation in the same way, but leaves the "story" intact.
A precis of "A Brief History of Time" (difficult to do) will leave you with understanding of the subject.
An abstract will give you a lot of facts, in a readable way, but you might not understand the point.
