The term open source software is used to refer to software whose source code is available freely subject to the terms of a licensing agreement. This is in contrast to most proprietary software that are available only in binary form.
Check out these examples of open source software from The Apache Software Foundation.
Open standards are standards that are created and maintained in an open manner, using a democratic approach, where no single individual or company controls the standard. This is the most important quality of an open standard. In addition, open standards are available to all, generally free of cost with no royalty or fee for creating an implementation conforming to the standard. Vendors may create either open source or proprietary software conforming to an open standard.
You'll find some open standards examples here: The Object Management Group's Open Process.
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