The Greek text of 2 Corinthians 7:10 according to the Nestle-Aland 28th ed. states,
Ιʹ ἡ γὰρ κατὰ θεὸν λύπη μετάνοιαν εἰς σωτηρίαν ἀμεταμέλητον ἐργάζεται· ἡ δὲ τοῦ κόσμου λύπη θάνατον κατεργάζεται. NA28, ©2012
The apostle Paul mentions ἡ λύπη (“sorrow”) twice. First, he modifies it by the prepositional phrase κατὰ θεὸν. Then, he uses it in a genitive construction: ἡ τοῦ κόσμου λύπη. What is the most accurate translation of each phrase, and how does the grammar (λύπη modified by a prepositional phrase v. λύπη in a genitive construction) affect the meaning of each phrase?
Was there a reason the apostle Paul preferred a genitive construction in the latter occurrence (ἡ τοῦ κόσμου λύπη) rather than, perhaps, another prepositional phrase such as ἡ κατὰ κόσμον λύπη? Or, does the latter occurrence only make sense when construed in a genitive construction?