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.
What is the difference between Agapi and agape?
Agape/Agapi (Universal Love)
The ancient Greek word agape is a very general term for love as a universal construct. The modern spelling is agapi. It doesn't refer to love for a particular individual, but to love in a more general sense. This is the love that one might have for every member of humanity.
How did ancient Greeks say I love you?
The modern Greek Σε αγαπώ, σ'αγαπώ, existed in ancient Greek, but it did not carry the same meaning as that of Se Filo. It was more an expression of love for things more idealistic.