Shareware is copyrighted software owned by the software author. Each program is accompanied by a file that explains how to register.
Freeware refers to programs that require no registration fee.
These programs come with no technical support. If the program does not work on your system, you're on your own. Some freeware programs are also what is called public domain software. This means that the author has released the copyright, and anyone may use the software for any purpose. Most freeware, however, is not public domain.