An argument frequently used by believers [is] to force unbelievers to soften their terms by accepting their opponents' definition; "Atheist" means without a concept of God that is logically convincing, not with proof that God does not exist.
"Atheist" is quite clear in its meaning of "somebody without a belief in God." It is more complex in its usage since it has often been used to blacken anyone with the slightest doubt about the teachings of religion.
"Agnostic" is a much more recent word than "atheist", coined by Thomas Huxley in 1869 to mean "without knowledge of God" and acquiring the usage of "being doubtful about the existence of God."