Refers specifically to an army division as a military unit. Not used for other meanings of 'division' such as corporate departments or mathematical division.
The division was deployed to the front line.
He belongs to an infantry division.
He was assigned to the 7th Division.
They newly organized a division.
The new soldiers were assigned to their respective divisions.
軍団 is a corps, a larger formation made up of multiple 師団 (divisions).
From 師 (し, 'teacher; military unit') + 団 (だん, 'group; corps'). The kanji 師 historically referred to a military unit of 2,500 men in ancient China, later adapted in Japan for the modern army division.