Self-justification is an attempt to be right by insisting and proving my rightness through logic, proof-texts, quotations and if necessary brute force. This is a self-focused orientation based on externals and intellectual prowess or even emotional intensity. It is what the Bible calls self-righteousness or a righteousness by works of the law.
True righteousness from God's perspective is an internally-oriented dependence on the faithfulness and goodness of God and a submission to the influences and promptings of the Spirit of God at the heart level. It is outward focused on the justifying of God instead of ourself. It is insisting that God is good all the time and forever and consistently without variation. Beyond that it is trusting in the identity that God has endowed on us as His children and resting in the value that He has for us, not in anything we can do or accomplish.