Ok, visceral afferents are fibers that supply your vessels and sm mm. While, special are for special senses (taste, etc).
This is the way I understand the TG p/w. That p/w is mad confusing. But, basically you have to divide it up into 3 stimuli.
1. Pain and temperature. So, the TG gangl sends its peripheral processes to all the areas of the face wherever it supplies. THe central processes come back and synapse in the lower 2/3 spinal TG nucleus in the pons. Ok, so I'll come back to what happens to these fibers.
2. Discrminitive touch. Likewise, the TG nucleus sends its central processes to the brain stem, and these synapse in the principle TG nucleus and the upper 1/3 of the spinal TG nucleus (probably don't have to know the latter). Now, both the principal TG nucleus and spinal TG nucleus decussate and send their axons to the contralateral side via dorso and ventral trigeminothalamic tracts (Dorsal is carrying information from D iscriminative touch, while ventral is carrying pain and temp.
3. Proprioception and motor. THis is kinda wierd. But, the ganglia for this, mesocephalic TG nucleus, is in the CNS, but it is analogous to the TG ganglia, and so it's peripheral processes are supplying the mm spindles and GTO in the mm of mastication, while its central processes are synapsing on ipsilateral TG motor nucleus,which is also in the pons. And, somehow they also synapse on the principal TG nucleus (but this may be a minor part). And, then the motor nucl sends efferents out to the respective mm where the proprioceptive stimuli is comming from. Oh, and the mesocephalic TG nucleus extends up to the MB. SO, the point is that a lesion above the pons, will give u contralateral loss of pain, temp, and touch to the face, while it should give u ipsilateral loss of the muscles (depending on where the lesion is, because the mesocephalic nucl extends from pons up to the midbrain). But, i think that is key.
Anyways, hopefully this made some sense.