This kind of software is free to anyone so it is possible to use, copy and distribute the basic software or the modifications of it. Free software usually goes with available source code and it can be included to free OS. In fact, the term free doesn’t always mean the price of the software: in some cases the copy of software is installed on the PC you buy and the price of it is included to the main price. Sometimes it means that there is a possibility to get a binary copy of the software for free. That is why before downloading software marked as free always look through the description of the product to make sure that it is actually free.
Open source software
This term is somewhere close to free software, though there are some restrictions and slight differences. However, almost all free software is open source and vice versa.
Public domain software
If you don’t see a copyright on software, consider it public domain software. Sometimes the source code is in the public domain, though copies or modifications are paid. Another situation is when the source code is unavailable, though the program is in the public domain. That kind of software cannot be free, as free one should have free access to the code. In fact, all programs are considered to be copyrighted so if you want it to be in the public domain, you have to take some steps.
In this kind of software it is not allowed to make changes to the copies of all versions with some safe possible adjustments. By this protection the program cannot be made proprietary.
It is advisable to use a single copyleft license for all users as it is good for the community, because two different copyleft licenses usually are incompatible.
Noncopylefted free software
This kind of software is given by author and user has a possibility to redistribute and modify the software.
Lax permissive licensed software
Here user gets a permission to use code any way he likes including distributing proprietary binaries.
These are only a few to name as the variations of software are really numerous.