Free software is free to use and distribute, but not always free of charge.
Freeware is free of charge, but copyrighted.
Shareware is commercial software, that can be trialware (limited in time) or demo (limited in functionality).
Open source is source open and free to use and distribute. The main difference with free software is that it might be copyrighted.
However, note that the term "open" and "free" don't exclude each other. So you can have licenses like GNU that are for free software that is also open source.
Here's a comparison:
Cost Redistributed Source Rights ------------------------------------------- Free software yes/no yes yes Copyleft Freeware no yes yes Copyright Shareware yes yes yes Copyright Open source yes/no yes yes/no Copyright
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