The correct answer is probably "both". What I would recommend is to take two consecutive photos and compare the output. This is going to be difficult because the earth is turning and the stars' relative position will change (rotate) as well as translate across your photo. If you mounted it on a sky tracking telescope mount it would be easier to make the comparison.
Another perhaps more simple method is to use a longer exposure. Stars will then be slightly streaked, and noise will not streak, so you can see how much, in general, your photos are including noise.
From my own experience in sky photography, there is almost always some noise. Sharpening brings it out. The best way to remove noise is to use multiple exposures on a calibrated tracking platform and use software to remove the points that only appear in one image.
It's not an easy question to answer precisely other than to say yes some of those points are most certainly noise because even in very expensive cameras there are some noise points. It is also highly certain that not all of them are noise. There are a lot of stars in the sky and many that you cannot see with the unaided eye so it is not surprising that a photo will reveal more than you can see.