At the next level of resolution, each muscle fiber is composed of many hundreds of myofibrils, which are elongated structures composed of repeating elements called sarcomeres. Each sarcomere is made up of interdigitating contractile elements, actin and myosin, that provide for muscle shortening by sliding relative to one another. The Z bands that divide sarcomeres in the aggregate produce the striated appearance that characterizes skeletal and extraocular striated muscles. Twitch fibers are more plentiful on the orbital side of the extraocular muscles, and tonic fibers predominate on the globe side. Cholinergic motor neurons supply both types of muscle fibers.
Experimental evidence suggests that the situation is probably much more complex.
Both types of fibers contract during all types of fast and slow eye movements. A Text Atlas. Surgical Management of Strabismus, 4th ed. The Neurology of Eye Movements. Binocular Vision and Ocular Motility.