Copyright laws can be a bit tricky and vary by location. Copyright and trademark are indeed very different.
There are many myths regarding what is protected and what isn’t. There are two aspects to an infringement modelers ought to consider. The first aspect is understanding what is protected. For example, in the US, modelers often believe that they may copy a model part for their own personal use, not for sale or profit, and therefore the copying is not an infringement. That is absolutely false. Copying a model part is considered copyright infringement and therefore is illegal. Copying a part deprives the holder of the copyright the revenue they earned in producing it. However, the second aspect, which has to do with enforcing the copyright and the holder recovering damages, comes into play. That is another can of worms entirely. But be aware that copyright holders often do act to protect their copyright and do recover damages.
A second myth is that the object must be registered in order to quality as copyrighted. That is also false. Registration helps with damage recovery but is not required under US law. Laws elsewhere may differ.
A third myth is that a US servicemember taking a photo as part of his or her official military duties retains copyright of the photo. Photos taken as part of official military duties are the property of the US Government, and unless specifically exempted, are normally considered in the public domain.
Short answer under US law from the US government’s Patent and Trademark Office (click here for more):
“Copyright is a form of protection provided by U.S. law to the authors of “original works of authorship” fixed in any tangible medium of expression. The manner and medium of fixation are virtually unlimited. Creative expression may be captured in words, numbers, notes, sounds, pictures, or any other graphic or symbolic media. The subject matter of copyright is extremely broad, including literary, dramatic, musical, artistic, audiovisual, and architectural works. Copyright protection is available to both published and unpublished works.”
The long answer under US law:
"Under the 1976 Copyright Act, the copyright owner has the exclusive right to reproduce, adapt, distribute, publicly perform, and publicly display the work. In the case of sound recordings, the copyright owner has the right to perform the work publicly by means of a digital audio transmission. These exclusive rights are freely transferable, and may be licensed, sold, donated to charity, or bequeathed to your heirs. It is illegal for anyone to violate any of the exclusive rights of the copyright owner. If the copyright owner prevails in an infringement claim, the available remedies include preliminary and permanent injunctions (court orders to stop current or prevent future infringements), impounding, and destroying the infringing articles, and monetary remedies.
“The exclusive rights of the copyright owner, however, are limited in a number of important ways. Under the “fair use” doctrine, which has long been part of U.S. copyright law and was expressly incorporated in the 1976 Copyright Act, a judge may excuse unauthorized uses that may otherwise be infringing. Section 107 of the Copyright Act lists criticism, comment, news reporting, teaching, scholarship, and research as examples of uses that may be eligible for the fair use defense. In other instances, the limitation takes the form of a “compulsory license” under which certain limited uses of copyrighted works are permitted upon payment of specified royalties and compliance with statutory conditions. The Copyright Act also contains a number of statutory limitations covering specific uses for educational, religious, and charitable purposes.”