what does these histogram tell you about the exposure
Notice how the patches show differently in the 2 histogram even when they represent the same lab values.
How those values are shown in a histogram vary depending on what that distribution of data represents in a color space.
(both are of jpg images and not raw)
So what? I don't see the point you are trying to make.
When using flash you have 2 exposures* to deal with - the ambient exposure* and the flash exposure*
The flash exposure* can be set automatically by the camera using ETTL or manually.
Even though the aperture, shutter speed and ISO are the same in both shots the total exposure* for Screenshot(5) was larger because more light from the scene hit the sensor due to the additional light added to the scene by the flash.
The 2 luminosity histograms are about what I would have expected for those shots.
* exposure - amount of light that struck the sensor per unit area while the shutter was open
Both articles are misleading. Capturetheatlas more because he determines the exposure using LR histogram, not the RAW one.
Artschoolportals article is better but I don't like the way they use PS Levels as example of exposure.
You are misunderstanding what is explained in those articles.
Consider this image with pure red (255,0,0), green (0,255,0) and blue (0,0,255) pixels on a pure white (255,255,255) background.
This is the RGB histogram for the image.
This is the luminosity histogram for the same image.
A histogram of any kind - RGB, Luminosity, whatever - is just a frequency count of some values - RGB, luminosity, the number of various coloured cars crossing an intersection etc etc etc - and nothing more.