Let's start by defining the 3rd nerve nucleus, fasciculus, and cranial nerve. The nucleus is located at the level of the rostral midbrain and is made up of the 3rd nerve neuronal cell bodies. These cell bodies give off a bundle of axons known as a fasciculus that pass inferiorly through the red nucleus and adjacent to the cerebral peduncle before exiting the brainstem as the 3rd cranial nerve.
Lesions of different locations along this pathway (i.e. the nucleus, fasciculus, or cranial nerve) will manifest with different deficits clinically.
A nuclear 3rd nerve lesion causes ptosis and ipsilateral mydriasis similar to a 3rd nerve fascicular or cranial nerve lesion. The distinguishing feature is involvement of the contralateral superior rectus and levator palpebrae superioris.
Remember the 3rd nerve nucleus innervates the ipsilateral medial rectus, ipsilateral inferior rectus, and ipsilateral inferior oblique along with the contralateral superior rectus. The levator palpebrae superioris is innervated on both sides by a common central subnucleus.
Due to the close proximity of the Edinger Westphall nucleus (housing the parasympathetic preganglionic cell bodies of the eye), the central levator palpebrae superioris subnucleus, and the 3rd nerve nucleus, a nuclear lesion often results in bilateral ptosis, bilateral superior rectus dysfunction, ipsilateral mydriasis, and ipsilateral dysfunction of the medial rectus, inferior rectus, and inferior oblique muscles.
The superior rectus subnucleus of the 3rd nerve sends fibers to the contralateral superior rectus. The fibers of the superior rectus subnucleus, however, decussate very close to the contralateral 3rd nerve subnuclei. Due to this close proximity, a lesion causing a 3rd nerve nuclear palsy is clinically never truly isolated and virtually always involves the decussating fibers from the contralateral superior rectus subnucleus. Hypothetically, the perfect lesion could only affect one 3rd nerve nucleus without affecting the contralateral decussating superior rectus fibers but that is not seen in practice.