If you create a sculptural work and then publicly display it, is that work published or unpublished?
If you post a photo on a website, is that work published or unpublished?
The answer is not as simple as it appears. For purposes of U.S. Copyright Law (17 U.S.C. § 101), publication means:
“the distribution of copies or phonorecords of a work to the public by sale or other transfer of ownership, or by rental lease, or lending. The offering to distribute copies or phonorecords to a group of persons for purposes of further distribution, public performance, or public display constitutes publication. A public performance or display of a work does not itself constitute publication.”
Thus, the key question, generally, is whether the copyright holder has authorized others to make a copy of the work.
In the case of the above sculptural work, the work probably is unpublished because a "public . . . display of a work does not itself constitute publication". However, it depends on where the work is being publicly displayed. If you display the work in an art gallery, which is offering the work for sale, then it would be published.
In the case of the photo posted on a website, the work may or may not be published. It depends on a number of factors concerning the authority to make a copy of the photo, such as the terms and conditions of the website, whether the website has any protection to restrict copying or use of the photo, and whether the photo is watermarked. Based on the facts, one court found that "posting the pictures to the website [without any protection to restrict copying or use of the photo] and making them accessible to others for distribution is considered a publication." William Wade Waller Co. v. Nexstar Broad., Inc., No. 4-10-CV-00764 GTE, 2011 WL 2648584, at *2 (E.D. Ark. July 6, 2011). But, another court found that posting images on a website was not publication. McLaren v. Chico’s FAS, Inc., No. 10 Civ. 2481(JSR), 2010 WL 4615772, at *1 (S.D.N.Y. Nov. 9, 2010) (unpublished) (citing Einhorn v. Mergatroyd Prods., 426 F.Supp.2d 189, 196-197 (S.D.N.Y. 2006) (noting that "making a work available [on the Internet], even assuming it constituted 'distribution,' did not involve 'sale or other transfer of ownership, or by rental, lease or lending.' ").
Determining whether a work is published or unpublished is important because it affects the window of time you have to register the work. If the work is not timely registered, then you could lose the ability to collect attorney's fees and statutory damages for infringement.