Can cat scan of chest and X-ray of chest have different results?

Yes. The chest xray is a regular xray and may not show everything that is present in the chest area. A ct scan has more cross sectional images with a higher resolution so that abnormal and normal findings can be viewed better.
Not unusal. The ct scan will provide much more information than the chest x-ray. Findings suspected on a chest x-ray may be confirmed or eliminated on the ct. Things that are inapparent on a chest x-ray are commonly demonstrated on the ct. The price is higher cost and higher radiation exposure of the ct compared to the chest x-ray.