Please note I am not an expert in the discussion on strict and pragmatic OMDoc, but I want to add some notes from our last discussion that helped me understand why we need both. Below you find the current definition of both terms:
This next version of OMDoc mainly adds the notion of “strict OMDoc” to serve as a canonical, semantic core of the OMDoc functionality. The current OMDoc vocabulary is re-interpreted as “pragmatic OMDoc” via translating into strict OMDoc.
We are currently still lacking usable editors for creating and maintaining our OMDoc corpus. Consequently, our users are still typing OMDoc or using our sTeX2OMDoc workflow to create OMDoc. To facilitate the editing process, we want to provide a less strict format, i.e. pragmatic OMDoc.The strict OMDoc also introduces some conceptual changes, which radical shorten the current OMDoc vocabulary, and aims towards a rather fundamental markup of OMDoc. However, in a more traditional view, these radical changes can cause disagreements with our previous users. Consequently, for the future we will maintain pragmatic and strict OMDoc. We might even introduce further pragmatic views on OMDoc targeted towards non-mathematicians and rather practical scenarios.
For further information see the OMDoc portal.