Does having anosmia mean that you have completely lost your sense of smell?

Yes. The term itself does mean that there is an absence of the sense of smell. Hyposmia is a diminished sense of smell. Some cases are secondary to nasal obstruction due to allergy, deviated septum with hypertrophic turbinates. A viral infection may injure the olfactory nerve twigs in the superior part of the nose. Very, very rarely a tumor of the base of the frontal lobe may be the cause.