The copyright may give certain conditions under which you may copy or even use the software. By default, a copyright stops anyone from modifying or redistributing the software. However, it is by no means compulsory to do this. If you do want to change the conditions of your copyright, you need to add a copyright message.
Free software licenses have very few restrictions. Some restrict you from changing the license, or have provisions to make sure the original authors get credit. Some try to make sure users aren't confused by competing versions of the software that claim to be the "real thing". Some have licenses to stop you hiding the source code from the user, or changing the license. Apart from these restrictions you can generally do anything you like with the software.
Semi-free software licenses are like free software licenses, but they restrict the anybody part to exclude certain groups. Often it is commercial users, but sometimes it is military use, or even users of a particular operating system. The people who are excluded usually have to treat the software as non-free software.
Licenses which say "if you like it, you are encouraged to ..." are not restrictions, merely suggestions on how to show your appeciation. If the license says you must do something, it is basically proprietry software, but with a different payment scheme. (If tempted to add conditions like this, consider if some people might find it expensive or even impossible to do such a thing. It might be cheap to send you a postcard or a pizza if you live nearby, but try it from another continent. Even email might be expensive. It's almost always best to simply suggest things - if they are cheap, many people will do them anyway).
Shareware restricts the distribution of source code, but allows distribution of binary code. It also puts a restriction on use, allowing you to use the program for a particular time period or only use certain features. Generally, you may not modify the binary code either.
Proprietry software restricts the distribution of source code, as well as distribution of binary form, use and modification. Usually you can do none of these things, although some licenses give a little more leeway.
Public domain software has no copyright at all - the author has given up any rights to the piece. This means you can do anything you want with it.
