We deal with the simpler subject first. A copyright is the simple assertion of ownership of certain types of intellectual property. Under the latest international copyright conventions, you do not even need to claim copyright for material you create. Unless you explicitly disclaim ownership, other people are allowed to use your intellectual property only in strictly defined ways, called fair use, unless you explicitly give them permission, called license, to do otherwise. So if you write a book or a piece of software, you do not need to put "Copyright c year" on it to own it. However, if you do not put this phrase on your writing, you may find it much more difficult to claim ownership in court if someone violates either your copyright (by claiming that, or acting as if, you do not own the copyright) or your license terms. The Berne copyright convention, an international treaty covering international copyright conventions and enforcement, requires participating nations to enforce copyright only
... if from the time of the first publication all the copies of the work published with the authority of the author or other copyright proprietor bear the symbol of a lower case "c" inside of a circle accompanied by the name of the copyright proprietor and the year of first publication placed in such manner and location as to give reasonable notice of claim of copyright.
The sequence (c) has been generally used as a replacement for the lower case "c" inside of a circle, but courts have not upheld that. Always use the word Copyright (in addition to the sequence (c), if you choose), when asserting your copyright. If a c character is available to you, it is best also to make use of that character, but do not neglect the word Copyright.
Copyright is not perpetual. All intellectual property eventually passes into the public domain; that is, the public eventually owns the copyright to the property, and any person can do anything with the property. No license terms are binding once the property is in the public domain. There is one twist: If you create a derived work based on public-domain work, then you own the copyright to your modifications. Therefore, although many old books are now out of copyright, their copyright having passed into the public domain, editors often make small changes here and there, correcting mistakes made in the original. They often then claim copyright ownership of the derived work that includes their changes. This copyright prevents you from legally copying the edited version, although you can freely copy the public-domain, out-of-copyright original.
Note that there are limits on what can be copyrighted. You cannot publish a book containing only the word the and then attempt to extort license fees from everyone using the word the in their books. However, if you create a sufficiently stylized painting of the word the, you would own the copyright to that particular representation, as long as it was sufficiently identifiable for you to show that prior art did not exist with the same representation. Although we are free to use the word the in this sentence, we would not be allowed to sell reproductions of your work without getting a license from you.
These limitations apply to software as well. If you are licensed to alter someone else's software and you make a trivial, one-word change, it would be absurd for you to claim copyright to that change. You would not be able to defend a copyright claim to that change in court; your contribution would be as much in the public domain as the word the is. However, if you add significantly to the software, you would own the copyright to your modification, unless, for instance, the copyright owners of the original licensed the software for modification with the license restriction that copyright ownership of all modifications revert to them.