So I'd like to better understand your notion of Local Context, and Global Context? Any hints?
As noted elsewhere in this thread, the local context of a process refers to the application of that process to a particular object or set of objects, usually images. The global context applies to the state of the PixInsight platform as a whole.
Examples of local processes: Invert, Rotate, CurvesTransformation, FourierTransform.
Examples of global processes: Preferences, ColorManagementSetup, NewImage, ImageIntegration, InverseFourierTransform.
There are also processes that can work in both contexts, such as PixelMath and StarAlignment.
For completeness, there is a third category of processes in PixInsight: Dynamic processes. A dynamic process (or dynamic tool) is capable of direct, real-time interaction with the graphical interface of one or more image views. It is customary to name dynamic tools with the word "Dynamic" prepended, such as DynamicCrop, DynamicBackgroundExtraction, DynamicAlignment or DynamicPSF, but there are exceptions such as CloneStamp and Annotation.
Also, is there any way of logging the transcript of a session to a text file for later review?
The log command allows you to generate console log files. Also as pointed out above, enter "help log" in the Process Console for a complete description of command line arguments.