Actually, they're not different. It's true you own the copyright in both photos but your copyright only extends to what you contributed, for example, the choice of subject matter, composition, lighting, etc. Your copyright does not extend to the statue, itself. If the statue and the image are protected by copyright, it would be a violation to reproduce them in your book (unless permitted under fair use principles). And, if you register your photos with the Copyright Office, you're required to disclose (and exclude) those items in your application because they are not original to you.
Photos of a statue. In some countries, for example, Canada, art that is permanently situated in a public place or building can be photographed and reproduced without permission. Not so, in the U.S. where unauthorized reproduction of a photo of a public statue can be costly -- as the U.S. Postal Service learned. (The USPS mistakenly used a photo of a Las Vegas imitation of the Statue of Liberty -- one with "a more contemporary, fresher face than the original" -- and the sculptor of the Vegas statue sued and recovered $3.5 million.) The reverse principle -- it is a violation of copyright law to create a sculpture of a photograph -- has also been followed by the courts.
In the real world. Few photographers of publicly-viewable statues need to worry about copyright lawsuits. The incidental appearance of a statue, for example, in a travel photo, a news photo, or an educational lesson is not likely to trigger a dispute and if it did, the reproduction would probably qualify as fair use. In addition, many statues are in the public domain and do not require permission (despite what some owners believe).