Yeah, it is often seen that many short sighted people have two different prescription in both eyes. The prescriptions are not in symmetry. It is normal which is caused by the improper use of two eyes, such as lying on bed or leaning on one side to read. Once you have got this problem, the eyeglasses must be matched with two different prescription to help you see the vision.
Because of glasses are using for correcting eye vision, we have two different size eyes, thus we have different degree of usage on each eye. Hence, for example, we could get myopia, but both eyes have different prescription. And there is a moderate to big difference which will be reflected in a different thickness of the lenses. You can see well through each side that might simply be your situation. If your left side lens thicker than that of right, which means the condition of your left eye worse than that in right eye.
Glasses thickness is varied with your myopia degree. The higher the myopia is, the thicker the glasses are. If two of your eyes are of the same myopia, the thickness of the glasses with the same material should be the same. But if different, that is ok.
There are many factors that can affect the thickness of glasses:
1. Myopia degree;
2. Refractive index;
3. Thickness of lens;
4. Type of lens.
In generally, the resin lens is lighter and thinner than glass one.
Well, according your description about your two lenses, yes they are different from each other in terms of how thick they are. So, my explanation for your question is that your eyes are both nearsighted, but the extent is different, so the doctor had to make you two different lenses so that your eyes will be able to see things clearly. It is just natural. People often have this problem, it doesn't matter to your vision. Just take it easy and don't make your vision worse.