What's the difference between ἀγάπη and στοργή?

Question

According to https://en.wikipedia.org/wiki/Greek_words_for_love ἀγάπη, among other things, refers to

Agape is used in ancient texts to denote feelings for one's children and the feelings for a spouse

while στοργή is explained like this:

Storge means "love, affection" and "especially of parents and children".[10] It is the common or natural empathy, like that felt by parents for offspring.

Sounds very similar (other meanings of the words are different). That these words share this meaning kind of contradicts the main point of this article

Ancient Greek philosophy differentiates at least four main conceptual forms and distinct words for the Modern English word love

Answer 1

στοργή derives from the verb στέργω, whose etymology

From Proto-Indo-European *sterg- (literally “to cover, to protect”)

may well give a clue to the connotation of protectiveness associated with the word.

So, στοργή summarizes the feelings of parents to offspring, but not vice versa (unless in the declining years of the former). My sense is that ἀγάπη is quite symmetric in this setup.

στοργή has a strong sense of familial affection. In early Christianity, the conceit of moving from ἀγάπη to στοργή suggested acquiring new quasi-family ties.

Answer 2

Storge (Στοργή) refers to the expression of Agape (Ἀγάπη) (but other types of loves too). In other words Storge is an act of, and Agape the feeling of. One cannot be feeling Storge (not in Greek (1), yes in English for affection and fondness), just express it.

(1) well, ok, maybe it can sometimes be worded as feeling it, but it really is strongly expression oriented.