In my experience, the presence of puffy nipples indicates excess breast tissue directly under the areolas -- there is no other possible cause. Puffy nipples alone can be considered gynecomastia. They can exist alone on a skinny body or can co-exist with extra tissue across the entire chest.
On the other hand, one can have excess tissues on a male chest without puffy nipples -- it is still called gynecomastia.
Dr Jacobs