What a wonderful question,
Yes, this is a common area of debate and you will meet people with different opinions.
My opinion is what you described as fat bulging anteriorly just superior to the inguinal canal but not entering the canal should be called posterior wall laxity.
If it is a young athlete I am happy to call it a sportmans hernia but only in a young athlete with athletic pubalgia symptoms.
If the fat goes through the posterior wall of the canal and enters the canal , expanding the canal and passing towards the superficial ring I call this a direct hernia.
My view is to only use the word “hernia” when a fascial plane has been broken and material passes through it. If it is not broken, but just weak I use the word laxity .
For example if the linea alba is very weak and bulges forwards when a person tries to sit up I call this linea alba laxity and rectus sheath divarication. If there is a hole in the linea alba and fat is passing from the peritoneal space into the subcutaneous space I call this a ventral hernia.
This is my logic.
Steve