At its most basic, a review can be positive or negative, but an endorsement is always positive.
A review’s primary purpose is to inform the reader and help him make a decision on whether or not he should spend his money and time on a book, while an endorsement’s primary purpose is to help promote a book.
Also, unlike a review, an endorsement doesn’t have a certain structure that includes an opening or lead, a brief summary of the story, and an evaluation. An endorsement is simply a 1-3 sentence recommendation of a book. Often, publishers approach well-known authors to write endorsements on an upcoming title. These endorsements, or parts of it, are often placed on the front or back cover of a book.
When reviews are positive, however, snippets of it can be used as endorsements for the book. So parts of a review can be used as endorsements, but endorsements aren’t reviews.
Obviously, the advantage of an endorsement is that it is always positive, but endorsements, unless they come from a well-respected source, are viewed by readers with suspicion, especially when written by fellow authors.
The con of reviews is that, of course, they might not always be positive, and authors may not always be able to use them as endorsements. But reviews are considered a more trusted resource and, unlike the endorsement, give the reader a well-rounded evaluation of a book.