What is the difference between a complete and incomplete hair lip?

See below. An incomplete hair lip means only the lip tissue is open at birth, a complete hair lip means the opening goes into the roof of the mouth (palate). Both are repairable by surgery.
Extent of defect. Hair lip is an old description of a cleft lip because it resembled a rabbit or hare. In incomplete cleft lips, the defect or cleft does not extend into the nose. In complete cleft lips, the defect extends into the nose.
Extent. Incomplete harelip may only involve the soft tissue, whereas a complete harelip can include the boney structures of the upper jaw or maxilla.