It comes down to just how different it is.
It is entirely possible for the atmospheric conditions to be similar enough, and the camera to be similar enough to produce similar effects, where it superficially appears to be the same, while the effects are still caused by the atmospheric conditions and camera.
Conversely, if it is shot at the same time, you can look for the same features.
For example, when 2 people take a picture of the moon at the same time, they see the same area of the moon illuminated; and when people take pictures of the sun, they can see the same sunspots in the same locations.
If it is genuinely a star being shot in focus showing features of that star, then you should be able to easily identify features on the star and track them over time, and these features should match between the 2 videos.
If instead it is a feature of the atmosphere and the camera being out of focus, then filming the star from different locations at the same time should show different (yet similar) features. This can mean that a feature lines up every now and then, but filming over a long enough period of time should show significant differences between the 2 views.
You want two videos of the same star, taken at the exact same time, from two different positions - maybe 10 feet apart is fine, since you don't specify any distance between the points?
It's odd you don't specify any sort of distance between each point, since you're the one who's asking ME to present such videos FOR you.....
What would be your MINIMUM distance, between each point? I'm assuming you don't meant 20 or 200 feet apart, even though it DOES meet your 'requirements'...
So you want two videos taken by two people, at the exact same time, at a
yet unknown distance apart from one another? I assume you want them to use the exact same camera, and settings, and so on?
Are you aware that two points on Earth separated by a FEW MILES can have different atmospheric conditions? Of course.
So when you ask for two videos of the same star, at the same time, simply being taken from two different points on Earth, will have differences in atmosphere, and temperature, and humidity, and so on.
Why do you think two videos of a star, taken in different conditions, at different angles, and so on, should somehow look 'exactly the same'? How would you quantify what 'the same' is, or is not? I suppose it's whatever you SAY it means, right?
How can you even
account for each point's different conditions, and adjust for them after taking the videos? The angle cannot ever be adjusted for, among other things.
All of your 'requirements', which are not yet defined, ignore the real problem, which is that you've NEVER SHOWN ANYTHING LIKE THIS ON EARTH, which is the FIRST REQUIREMENT HERE.
You say this is caused by XYZ, without EVER showing any examples of it on Earth. Your blurry crap with shaking cameras is NOT an 'example' of it, but I guess that's the best you could do, even if it's worthless crap....
The first problem, is that ALL the stars move constantly, change shape and or details, change in color, and are all different, to various degrees, for every OTHER star.
So that's millions of stars, which ALL are moving, changing shape, etc. While none anywhere on Earth, among trillions of objects....
There has NEVER been a light, or an object that emits light, or any object, PERIOD, which has appeared to constantly, endlessly move, on the Earth.
If you cannot tell the difference between YOUR example, and how stars look close up, there's no point in trying to have an honest debate with you.
But, I hope you are honest enough to see they are not even close to the same....