What is the distinction between worldly and godly sorrow?

Mike Davenport explains in this video that there is a significant difference between worldly and godly sorrow. Worldly sorrow is a sorrow that may lead to repentance, but it is primarily concerned with self and how others think of them. In other words, the focus is horizontal - the offender is concerned with our their sin impacts themselves or others but does not consider what God thinks of their sin. 

In contrast, godly sorrow is vertical-focused. It asks how we have offended God. We realize that our sin doesn’t just affect ourselves or others, but that when we sin, we also sin against God. 

Psalm 51:4 (NKJV) – “Against You, You only, have I sinned, and done this evil in Your sight—that You may be found just when You speak,[a] and blameless when You judge.” 

There is a big difference between worldly sorrow and godly sorrow. Worldly sorrow is a sorrow that may lead to a repentance, but it's horizontal. It's concerned with me and with how men think of me. Whereas godly sorrow is vertical. The main concern of godly sorrow is how I have offended God.

And we see this in Psalm 51 with King David. King David said, against you and you only have I sinned. Was that to say that he had not sinned against Uriah, that he had not sinned against Bathsheba? No, it did not mean that whatsoever. But he realized that his sorrow was so deep that it wasn't just concerned with the ways that he had wronged and sinned against his fellow man, against Uriah and against Bathsheba.

But he realized there was something more important. And it was a godly sorrow that led him to say, against you, O God, and against you only, have I sinned and done this great wickedness. And so I think you