As others have noted, the ISS orbits the earth extraordinarily quickly, and that explains the discrepancy. However, there may still be a small error in your simulation.
Whether or not there is an error depends on where you intend the "camera" to be. My suspicion is that your simulation was created as follows:
- Make a sphere at the origin, inclined 23 degrees.
- Texture the sphere to look like the Earth.
- Put a light at some distance along, say, the z axis.
- Place the camera somewhere on the z axis.
- Spin the earth at one rotation per 24 hours on its inclined axis.
- Capture 12 hours of video.
But that's not a realistic simulation of the earth, for the somewhat obvious reason that the Earth is in orbit around the Sun.
People who have not studied astronomy or horology are often surprised to learn these two facts:
- The time between two noons at a given point on the Earth is not 24 hours.
- The time it takes for the Earth to spin on its axis is not 24 hours either.
Surely that's what you were taught, but that is completely wrong. (In fact, my grade 12 physics teacher of all people had a bunch of completely wrong beliefs about the length of the day and would not believe me when I tried to explain it to him. If science teachers cannot be bothered to get it right, it is no wonder that students don't get it right either.)
To take the second point first: the Earth spins on its axis in 23 hours, 56 minutes and 4.1 seconds. The amount that nearby stars move relative to each other in a day is incredibly small, so let's pretend that it is zero, and that your camera is fixed in place with respect to those stars. From that perspective, in the course of a day you would see two things:
- The Earth would rotate exactly once in 23h56m4.1s -- one sidereal day
- The Earth would move approximately 1/365.25th of its orbit around the sun.
It is the combination of those two movements that makes it appear to us -- prisoners of gravity, stuck to the surface of the Earth -- that the day is on average 24 hours long. (Notice that one sidereal day is 1/365.25th shorter than a mean solar day; that's not a coincidence!)
Plainly your camera cannot be fixed relative to the "fixed stars" because the Earth is getting neither bigger nor smaller.
Suppose instead you simulated the Earth going around the Sun, and you placed your camera on the line between the Earth and the Sun, pointing at the Earth. Now would we observe the rotation to be exactly once every 24 hours, assuming we sped the Earth up to rotate once a sidereal day?
No, we still would not observe the day to be exactly 24 hours noon to noon, because we've forgotten something else. The Earth orbits in an ellipse, not a circle, with the Sun at the focus, and orbits are faster when they are closer to the Sun. That means that some times of the year we have noon-to-noon times that are slightly longer than 24 hours, and sometimes slightly shorter, and they average out to 24 hours over a year. This is called the mean solar day, and the relationship between the mean solar day and the time it actually takes to go from noon to noon is determined by the equation of time. Our 24 hour clocks are running ahead of the Sun in the northern hemisphere's winter and summer, and behind in spring and autumn.
Now suppose you simulated that; would your simulation now be accurate? It depends on the level of precision you need to reach. For example, the Earth's orbit is affected by the position of the Moon. The Earth's orbital path does not pass through the center of the Earth; it passes through the barycenter of the Earth-Moon combination. Also, the tides caused by the Moon are causing the Earth's rotation to slow down. And there are wobbles in the Earth's motion caused by various factors, and these all affect the length of the day.
So it all comes down to how accurate you want your simulation to be. If you just want to give a sense of how fast the Earth rotates, your simulation is fine; it is certainly has less than a 1% error. If you want to accurately simulate the relationship between the Earth and the Sun, you'll need to take more factors into account.