In North America, the mandolin family follows the same terminology as the violin family and are tuned in the same range.
violin - mandolin
viola - mandola
cello - mandocello
bass - mandobass

It gets a bit confusung when the mandolin family instrument has no corresponding violin family instrument.
An Octave mandolin would be an octave lower than a mandolin.
An octave mandola (mandocello) would be an octave lower than a mandola.
There are many confusing names for these "long neck mandolins". I've heard them called bouzoukis, Irish bouzoukis, citterns, octave mandolins, octophones, monster mandolins, mondothings... Different folks define different long necked mandolins bassed on whether or not they have octave tuning, how long the necks are, how many courses they have... I don't like the terms bouzouki or cittern, since there are already instruments with that name. The Greek bouzouki has 3 or 4 courses and a bowl back and, quite often a magnetic pick-up.
Grit Lasken used to make what he called "long neck mandolins". I believe that he used that name regardless of the number of courses or the neck length or whether or not there were octave courses.