The two things are completely different entities.
Davids genuine car will have jacking points fitted into the sills as per this picture
These are a square section tube which is most likely located slightly farther forward, closer to the balance point of the chassis which accepts a jack which has a square peg, the positive location of a square within a square will help prevent the jack twisting & the car rolling forward whilst it is lifted off of the ground. In this scenario you would lift one side of the car off the ground first to change the wheels on that side before swapping & lifting the second side independently. So no, you wouldn't lift both side of the car at the same time using these points
Sill stands are a totally different entity where the stands are located into round tubes & used as pairs which allows either end of the car to be lifted independently of the other using a trolley jack as the lifting device. In this case the rear of the car could be lifted first & then because the mounts are tubular thus allowing the car to rotate around them then the front of the car can then also be lifted to the same height. In this case the rear mounts are farther back than the balance point to prevent the car tipping backwards as suggested earlier. See this pic of the Perez car for reference.
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