Oxforddictionaries.com says counselor in US and counsellor in Britain.
Section 3 indicates the section 1.3 is the ranking in the embassy, and that of consulate not part of 1.3. Hence, it is understandable that a consul general is deemed about the level of minister or counsellor.
Note: Ambassador Raymond Burghardt, Chairman of the American Institute in Taiwan. AIT, Oct 21, 2013. https://www.ait.org.tw/en/chair-burghardt.html
("Prior to his arrival in Taipei, Burghardt was Consul General in Shanghai (1997-99)" )
Born in 1945, he is 71 years old.
(3) 石秀娟, 薄瑞光專訪》美國非常尊重台灣 「非美中關係的附屬品」 http://www.storm.mg/article/166014
("在13日接受《風傳媒》專訪 * * * 擔任AIT台北辦事處的處長2年、AIT理事主席10年半的薄瑞光 * * * not some kind of appendage, or sub-piece of US-China relationship * * * [photo caption:] 《風傳媒》專訪即將卸任的美國在台協會理事主席時,AIT處長梅健華(Kin Moy,右)中途也特地敲門進來,提前請大家吃月餅")
My comment: Not only have I not heard of "sub-piece," but I am unable to find such a word in the Web.