EDIT: My question was based on a false premise and now I understand how I was wrong with my assumption.
First of all, your definitions are very partial and do not encompass the entire mindset of all atheists and agnostics. Secondly, there is no Ultimate Dictionary that defines words for time and eternity. For that reason, words and their definitions keep changing. At one point in time, “atheist” meant a person who denied the existence of God. These days, “atheist” is generally defined by atheists themselves as meaning “lack of belief in god or gods.”
Agnostic originally meant that it is impossible to know whether or not God exists. These days, many people use it to mean that they personally don’t know if God exists. Many who move from faith in the Christian God to atheism due to conviction, in their search for truth, divide the deconversion process into stages of first being agnostic before atheist. These people think that “atheist” means to be sure that the Christian God does not exist. Others, however, claim that it is impossible to know whether or not a god or gods exist but they lack all belief in any god or gods. In other words, they personally do not hold any belief whatsoever in any supernatural entity but they think it is impossible to know for sure that no such being lurks in some corner of the universe.
I think this latter may take ideas from Deism, the belief that God created the universe, then retreated to let things take care of themselves. I personally think that makes sense only if we don’t accept evolution theory, etc., but who am I to dictate what others should believe. The point of this post is to explain why or how people can logically self-identify as atheist agnostic or agnostic atheist. This is why. The reason people self-identify as Christian is just as convoluted. “Christian” logically means “believer in Christ.”
Some believe in Jesus Christ as Son of God and personal Saviour. Some who self-identify as Christian believe in Jesus as being accessible to humans through his Mother Mary and other saints. Others believe in Jesus as Son of God or as Prophet but do not believe in his atoning blood; some do, however, self-identify as Christian. Others believe in Jesus as one of the most important prophets but not divine; many of these self-identify as Muslim.
Therefore I suggest that no sect or group can accuse another of being confusing in their self-identification labels.