Freeware is software, program or application that is freely downloaded, used and shared on any scale. Once downloaded, the end user usually never experiences any need to pay for the software.
The choice to release a developed program as a free product is usually for the purpose of providing a free version that has limited features with the aim to get the end user to buy the full feature version.
Some software providers offer Freeware which is full featured with no aim to persuade you into buying a better version of it, some instead do so to increase brand awareness and reputation for good programs.
Opensource is software which allows for users to contribute to the source code of the software and help with integration of the program with other software or services. Similarly, to Freeware, opensource software is mostly free. For example, WordPress (Self-Hosted) is Opensource and free.