Aside from some different copyright statements, both Motif and OpenMotif share the same functionality and source code. The primary difference is the software license for each piece of software. OpenMotif source code and binaries are distributed royalty free under The Open Group Public License as long as the underlying operating system is open sourced. Motif is made available under the standard Open Group software licenses and has both source code and royalty fees. In short, if you are using Linux, or some other open source operating environment, Motif is open and freely available, hence the use of "OpenMotif".
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