RoseKavalierThere are 2 components to randomness that were modified by HD+ somewhere around 3.50 (I forget exactly when)
1- random seed
2- random number generation

In SoD_SP, they are respectively named:
1- Original RNG
2- Original Obstacles

The names don't reflect entirely what they do (I may change the wording and description), the reason is because I wanted names that reflected the repair of "broken" single player features by HD+. In your videos you have one turned on, the other turned off, so you are getting a mix of original H3 and HD+. Calls to RNG will also call Random Seed, and modify future outcomes - creature animations in the window calls RNG(1, 100) which is why you can get some different results.

Essentially, you are getting these results because of HD+, mixed with vanilla H3 at some points.
It's up to you to decide how you want to use these; I just want to clarify that this is not really due to SoD_SP behaviour, there are no modifications to this part of code only restoration of vanilla.