Any office, department, board or agency provided for in this article with a name or with powers and duties which are the same or substantially the same as those of any office, department, board or agency heretofore existing shall continue to exercise its powers and duties, unless and until otherwise provided. Any provision of law, rule, regulation, contract, grant or other right relating to any such formerly existing office, department, board or agency shall, so far as not inconsistent with the provisions of this article, apply to any office, department, board or agency provided for herein.