Question: Does "wheat-free" mean the same thing as "gluten-free"?
Absolutely not. In fact, in many cases foods labeled as "wheat-free" contain some gluten.
Gluten is found in wheat, but it's also found in the grains barley and rye. A food labeled as "wheat-free" still can contain either of those grains or ingredients derived from them.
Food labeling laws in the United States require manufacturers to disclose wheat, since it's considered one of the major allergens, but not gluten.
A food labeled "wheat-free" that contains gluten ingredients would be safe for someone with a wheat allergy to consume, but not for someone with celiac disease or gluten sensitivity.