Apodictic law refers to timeless divine commands or laws in the Old Testament which are necessarily or demonstrably irrefutable truths. Thus it is incontrovertible expressing proscription and injunction, since it is divinely revealed, as in the Ten Commandments (You shall…, You shall not… etc.) So, Apodictic Law is established by God himself and beyond dispute.
On the other hand, Casuistic Law refers to the applied law of God in different cases. When someone commits sin or crime, the he/she will be penalized accordingly. i.e. if s/he does such and such, then this kind of penalty or punishment will be inflicted upon him/her. Thus, “Casuistic law in Israel is often the development of laws for particular personal and societal needs in light of God’s holy and eternal apodictic law.”1
- Biblical Nuggets: Casuistic Law (cafn.us)