I don't know...
Officer's Cook seems to be/have been
a general term.
In Thetis' log (http://oldweather.s3.amazonaws.com/ow3/final/USS%20Thetis/vol004of024/vol004_006_0.jpg
) it lists several different kinds of cooks, although Thetis 'only' has 1 Ship's Cook, 1 Cabin Cook, and 1 Ward-room Cook.
Definitions from: http://www.history.navy.mil/faqs/faq78-3.htm
(for US Navy
, so there may be some differences here)
Ship's Cook (Changed from Cook 1838; changed to Ship's Cook 1c, 2c, and 3c 1893; changed to Commissaryman 1948.)
Cabin Cook (Changed from Officer's Cook 1864; changed to Officer's Cook 1c 1923.)
Ward-room Cook (Changed from Officer's Cook 1864; changed to Officer's cook 2c 1923.)
Steerage Cooks (Changed from Officer's Cook 1864; changed to Officer's Cook 2c 1923.)
Warrant Officer's Cook (Changed from Officer's Cook 1864; changed to Officers Cook 3c 1923.)
Cook to Commander-in-Chief - only on a flagship (Changed from Officer's Cook 1864; disestablished 1921.)
Officer's Cook - Established 1838; changed to Cook to Commander-in-Chief, Cabin Cook, Wardroom Cook, Steerage Cook, and Warrant Officer's Cook 1864.
(I hadn't associated Steerage with Officers
In the United States military, a Warrant Officer
(grade W-1 to W-5) is ranked as an officer above the senior-most enlisted ranks, as well as officer cadets and candidates, but below the officer grade of O-1 (NATO: OF-1). Warrant officers are highly skilled, single-track specialty officers... - http://encyclopedia.thefreedictionary.com/Warrant+Officer+%28United+States%29
Since, strictly speaking, the captain is not a wardroom officer, I wonder if the Cabin Cook is the captain's cook