The interpretation can be quite broad. In my view, a gift tends to be something you receive immediately, whereas an advantage can be something you receive in the future. That's how I see it, anyways. You can receive a gift right away, for example, a bottle of wine or a painting. An advantage, however, can be a job offer when someone retires—after two years in the case of a minister or after one year in the case of other public office holders.
I like the expression
“undue advantage.”
The word “undue” is perfect.
An advantage can be gained from being a person's friend. For some people, being friends with a person constitutes an advantage. For others, the advantage could be career advancement.