When you pursue rightness rather than righteousness, you are concerned with being correct at any cost. Correct in the eyes of man, that is. Righteousness, on the other hand, is concerned only with what God thinks. No opinion of man matters. 
Let me present a hypothetical situation. Suppose you get into a disagreement with someone over a business transaction. Suppose the other person cheated you out of some money.

Then suppose the Spirit of God tells you not to worry about it, but to let God take care of it instead. At that point you're faced with a decision. Do you do whatever is necessary to prove that you are right?

After all, you've been cheated! Or, do you stand in the righteousness of God and trust Him to move on your behalf?

The first course is to pursue rightness. The second course is to choose righteousness.

When you pursue rightness rather than righteousness, you are concerned with being correct at any cost. Correct in the eyes of man, that is.

Righteousness, on the other hand, is concerned only with what God thinks. No opinion of man matters.

The two differ in other ways as well. Rightness is usually self-centered. It says, "I've got to look good before man in order to feel good about myself." When you have that attitude, you'll fight to your last breath to prove that you're right and the other person is wrong.

Rightness seeks self-gratification and approval from God through good works. In contrast, righteousness recognizes that you are accepted based on what Jesus has done through His blood and the cross.

The bottom line is, righteousness seeks to please God rather than self.

How does righteousness please God? By faith! Romans 3:22 tells us that righteousness is "by faith." And Hebrews 11:6 tells us that without faith it is impossible to please God.

Backed Up By Righteousness
"Seek ye first the kingdom of God, and his righteousness and all these things shall be added unto you" (Matt. 6:33).

When you are bent on proving your "rightness" to other people, you leave God out of the picture. You're on your own. At that point you're easy prey for anything the devil wants to throw at you.

But when you seek God's righteousness first and foremost, God is committed to back you up every step of the way.

The first approach puts you in bondage to other people. The second places you in the liberating service of a loving God.

"But Pastor Dollar! You don't know what that person is saying about me! What about my reputation?"

Look. If you'll take care of your character, God will take care of your reputation. Just stay in the righteousness of God and operate in the fruit of the Spirit. When all is said and done, God will back you up and your reputation will be stronger and better than ever.

I'm not implying that reputation isn't important. It's vital that we, as people who name the Name of Jesus Christ, abstain from the very appearance of evil.

I'm simply saying you don't have to run around defending yourself when people accuse you falsely or tell lies about you.

Take care of your character and God will look after your reputation. Psalm 9 guarantees it:

When mine enemies are turned back, they shall fall and perish at thy presence. For thou has maintained my right and my cause; thou satest in the throne judging right.
(vv. 3-4)

We all have enemies. Just don't get your eyes on them. Keep your focus on the One sitting on the throne. That vision will fill you with confidence in knowing that Almighty God is taking up your cause.

That means you don't have to get in the flesh and do something—that will probably make things worse, anyway.

Source: Rightness vs. Righteousness by Creflo A. Dollar Jr..
Excerpt permission granted by Creflo Dollar Ministries