Defination's

Definition of Shareware:

Shareware distribution gives users a chance to try software before buying it. If you try a Shareware program and continue using it, you are required to register it (or purchase the Licensed version).

Copyright laws apply to both Shareware and retail software, and the copyright holder retains all rights, with a few specific exceptions as stated below. Shareware authors are accomplished programmers, just like retail authors, and the programs are of comparable quality. (In both cases, there are good programs and bad ones!) The main difference is in the method of distribution. The author specifically grants the right to copy and distribute the software, either to all and sundry or to a specific group. For example, some authors require written permission before a commercial disk vendor may copy their Shareware.

Shareware is a distribution method, not a type of software. You should find software that suits your needs and pocketbook, whether it's retail or Shareware. The Shareware system makes fitting your needs easier, because you can try before you buy. And, because the overhead is lower, prices are lower also. Shareware has the ultimate money-back guarantee - if you do not use the product, you do not pay for it.
Definition of Freeware:

Freeware distribution gives users a chance to try software and continue to use it for no payment at all or just for some acknowledgement (a thank you note, a postcard, some suggestions, comments, etc.).

Copyright laws apply to both Freeware and retail software, and the copyright holder retains all rights, with a few specific exceptions as stated below. Freeware authors are generally accomplished programmers, just like retail/shareware authors, and the programs are of comparable quality. (In both cases, there are good programs and bad ones!) The main differences is in the method of distribution and the fact that there is no charge for using the software. The author specifically grants the right to copy and distribute the software, either to all and sundry or to a specific group. For example, some authors require written permission before a commercial disk vendor may copy their Freeware.
Definition of Public Domain:

Public domain is a bit different from the above two. Generally the source code for the software is included and the author specifically grants you the rights to copy and distribute the software. In addition you can modify the software or include the modified code in your own programs (non commercial usually) for an acknowledgement.
The copyright holder retains all rights to the original code, but the modified code belongs to the new copyright holder. As this depends on author, you should read the specific instructions issued with the respective software.