Self-denial is when you rely on yourself and your credibility and attempt to carry something out in the power of your "self." "Denial of self" is when you realize your "self" will be used to carry out an assignment, but you know the reality is that it's the credibility of God and His Holy Spirit that will be your reliance.
Moses was called of God to deliver the children of Israel out of Pharaoh's tyranny. Moses asked God, "Whom do I tell them that is sending me?" Moses began to see how his own credibility would be called into question. After all, he was known for killing a man and had a past that didn't really line up with the qualifications he thought he needed to fulfill that call. This reminds me of many of us today. God calls us for an assignment that He desires to be fulfilled, and then we begin to examine "self" and disqualify ourselves because of our past, because lack of education, lack of experience, bankruptcy, divorce, and the list goes on an on. Believing this lie of disqualification causes a deception of trying to fulfill a call and an assignment in our "self." When we try to evaluate self to fulfill a call, we make the mistake of relying on "self" to carry out the assignment. God's response to Moses was this: "Clearly tell them I AM hath sent you." In others words, I will use your "self" but I - God, the great I AM - will carry it out.
Thats the authority and power He refers to when He says, "Go in My name."
So, when we receive a call, the first thing we have to realize is that it's God's credibility and reputation we are going to operate in. Secondly, "self" will be used, but will not be the source of the power to carry it out.
So, what are you operating in?
Self-denial or denial of self?