Does finding a shadow on a chest X-ray always mean that the person has lung cancer?

Not always. But further workup with ct scan and possibly other tests is required.
Shadows mean. You have to find out the cause. All we used to have were chest x-rays. Only recently has there been proof that screening older smokers are ct scans better at detecting than chest x-rays. That study looked at 32, 000 case; found 4000 shadows, but only 400 cancers for round figues, but reduced lung cancer death by 25%. So, some, even most, shadows are not cancer.
No. A typical chest xray is not very specific. An abnormal chest xray should be followed up with a chest ct scan. A ct scan is very good to evaluate and find chest abnormalities.