The Convention Of States lawyers have lied to you.
Article V Convention supporters claim they aren't pushing for a Constitutional Convention. Their lawyers have agreed. However, Blacks Law Dictionary, the definitive source for lawyers, shows where an Article V convention IS a Constitutional Convention:
http://thelawdictionary.org/constitutional-convention/ (Blacks Law Dictionary) Constitutional Convention – A duly constituted assembly of delegates or representatives of the people of a state or nation for the purpose of framing, revising, or amending its constitution.