No, gluten free does not always mean wheat free.
Some manufacturers use wheat that has had the gluten removed to make gluten free foods.
A typical example is many gluten free breads and rolls have wheat in them that has had the gluten removed, they do this to make them more like ordinary bread or rolls. This makes it a bit of a challenge as you need to read the ingredients list on gluten free foods carefully, to ensure that you have not got one that is using wheat with the gluten removed. So you need to exercise a bit of caution as gluten free foods are not necessarily safe for you to eat if you need to avoid wheat. Bread flour for breadmaking machines is no different from bread flour for hand baking, it contains wheat, so if you have a wheat allergy then it should not be used. There are many alternative flours available that can be made into bread, rolls, cakes etc.