Totally agreed. In short, harmonics, with each variable (powder burn speed and pressure) making it's own changesYou've asked a question with so many different variables. I'll try to answer a few....but entire books could be written on the topic.
The barrel is a big tuning fork. The powders have different burn rates and different pressures at different points in the process of burning. The bullet is propelled at different rates. Therefore, the muzzle is at different positions of the "whip" when the bullet exits. Turbulence is different as the bullet exits the muzzle. The powder reacts differently within the case based on the case fill, etc.
In addition to the things mentioned, besides the issue of heat of the powder when firing the cartridge, there can be significant differences with just the one powder you have on your shelf due to how you handle the powder. I'm referring to the humidity in your environment and its effects on the powder when exposed. Gun powder can absorb or lose moisture content to the atmosphere, and that can occur rather quickly, particularly when there's a large difference. For example, I live where relative humidity is often below 20%. When it's low the atmosphere acts like sponge and sucks moisture right out of the powder rather fast. Powder that has it's moisture content reduced will result in a faster burn rate thereby increasing velocity and upsetting the expected group sizes. If RH is the opposite and way high (like 90%), the powder acts like a sponge and will absorb moisture resulting in slower burn rate with slower MV's.If you have the same case prep, the same primer, same bullet and tension and seating depth but different powder they shoot different size groups, using the same rifle. What makes the powder do this?