People very often confuse between these three types of software and often use interchangeably. In some context this interchangeable usage might indeed be correct but there are very distinct differences between these classes of software. Our requestcd service only supports Free Software and Open Source Software and we frequently get requests for Freeware which we politely refuse citing the difference between Free Software and Freeware.
Wikipedia defines 'Freeware' as a software that is fully functional for an unlimited time with no cost, monetary or otherwise. There could be restrictions on the type of use though. The software license may impose restrictions on the type of use including personal use, individual use, non-profit use, non-commercial use, academic use, commercial use or any combination of these. For instance, the license may be "free for personal, non-commercial use".
The corresponding 'definition of Free Software by Free Software Foundation defines Free software or software libre as software that can be used, studied, and modified without restriction, and which can be copied and redistributed in modified or unmodified form either without restriction, or with minimal restrictions only to ensure that further recipients can also do these things.
An Open Source Software on the other hand is a software whose source code is available without any restrictions on distribution and modification for the end user. There could however be restrictions on usage imposed by the license of the software. The Open Source Definition by the Open Source Initiative also defines certain pre-conditions for a software to be defined as Open Source by the OSI definition.
While Freeware is differentiated by the monetary aspect of software, Free Software is differentiated by the Freedom associated with software & its source and Open Source is differentiated by the Openness aspect of software & its source. Consequently a Freeware can be Free Software or Open Source but it does not have to be either. Free Software is always Open Source, because the freedom to study and modify requires you to have access to source code. Both Free Software and Open Source does not require the software to be free of cost, and hence does not have to be Freeware but more often they are than not.