According to The Free Dictionary:
Eager beaver: One that is exceptionally, often excessively industrious or zealous
To be more catholic than the Pope: To adhere more stringently to Roman Catholic practices and doctrine than is required by church doctrine; - usually used in a negative sense to mean, to be excessively pious.
We Persians use the second expression equal to the Persian expression which is: A bowl which is hotter than the soup that means a person who cares to the others business specially instead of people who are responsible about more than them or more than his/her own business.
So I want to know is it correct to consider two above expressions as synonyms or equal to each other or not?