Special operations are military operations that are "special" or unconventional and carried out by dedicated special forces and other special operations forces units using unconventional methods and resources.
A military operation is the coordinated military actions of a state, or a non-state actor, in response to a developing situation.
United States Special Operations Forces (documentary) by DEVGRU5022
Special operations may be performed independently of or in conjunction with, conventional military operations.
Special Operations Helmet Cam Firefight in Afghanistan by FUNKER530 - Veteran Community & Combat Footage
The primary goal is to achieve a political or military objective where a conventional force requirement does not exist or might adversely affect the overall strategic outcome.
Special operations are usually conducted in a low-profile manner that aims to achieve the advantages of speed, surprise, and violence of action against an unsuspecting target.
Special ops are typically carried out with limited numbers of highly trained personnel that are adaptable, self-reliant and able to operate in all environments, and able to use unconventional combat skills and equipment.