Based on the description of doyagao and smug, I can't really see the difference between the tags. The wiki page for doyagao describes it as "a facial expression conveying a self-satisfied, cocky, or smug attitude", while smug is described as "exhibiting or feeling great or offensive satisfaction with oneself or with one's situation", which sound synonymous with each other.
Is one a subset of the other? The same? Different?
If someone could provide clear examples (and possibly put it on their respective description pages) it would be appreciated.