Does finding a shadow on a chest x-ray always mean that the person has lung 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.

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.

Not always: But further workup with ct scan and possibly other tests is required.