What is the difference between Tethyan Himalaya and Trans Himalaya?
I've seen the two terms being used interchangeably, but geologists recognize them as geologically distinct terrains. Their geographic locations and geologic context has been annotated in the satellite imagery below.
The Indus Suture is the zone of collision between the Indian and Asian tectonic plates. It contains broken pieces of oceanic crust and deep sea sediments which were uplifted and jammed between the colliding continents, forming a sort of a geologic no-man's land. The Tethyan Himalaya are the ranges immediately south of the Indus Suture. They are the deformed rocks of the Indian plate. The Trans Himalaya are the ranges north of the Indus Suture made up of a variety of rocks of the Asian plate.
The Tethyan Himalaya is a pile of Paleozoic and Mesozoic sedimentary rocks which was deformed into a fold and thrust belt during the early stages (45-35 million years ago) of the India Asia collision. At places, the sedimentary cover has been stripped away by erosion and high grade metamorphic rocks formed deep in the crust have been exposed. These 'windows' are known as gneiss domes since the sedimentary cover rocks have been arched up during uplift and exhumation of the high grade rocks. The area around the famous Tso Moriri lake is one of the best examples of a gneiss dome.
If your are traveling in Zanskar, Spiti, Lahaul, upper reaches of Kinnaur, and near about Milam and Panchachuli Glaciers, you are in the Tethyan Himalaya.
In the late Cretaceous (100 million years ago), the leading edge of the Indian plate began subducting underneath Asia. As the plate dove deeper it heated up and released water, which triggered the formation of magma in the upper mantle of the Asian plate. This magma rose and assimilated rocks from the Asian lower crust. It then intruded older sedimentary and metamorphic rocks of the Asian crust and solidified as giant bodies of granites and granodiorites (containing calcium rich feldspars). These large granitic intrusions or 'batholiths' range in age from 100 million years to about 50 million years ago. One example is the Ladakh Batholith on which the town of Leh sits. Some of this magma also erupted on the surface through volcanoes. The rocks of Khardungla Pass are remnants of this ancient volcanic terrain.
A similar situation today is along the western South American margin. There, subduction of the Nazca Plate underneath South America has triggered large scale magmatism and formation of giant batholiths of the Andes Mountains.
Another impressive geologic feature of the Trans Himalaya is the Karakoram Fault Zone. It is a NW-SE aligned right lateral strike slip fault where crustal blocks have been sliding past each other since about 18 million years ago, resulting in a 150 km of offset of rocks. There has been some vertical movement also along this fault and this uplift has resulted in the formation of the Pangong Ranges where high grade metamorphic rocks have been exhumed from a deeper crustal level. The Pangong Lake is a drowned river valley formed by the damming of the river on its western end due to fault uplift.
Strike slip faults have been in the news recently. The devastating earthquake in Turkey and Syria was caused by movement along the left lateral strike slip East Anatolian Fault.
The India Asia collision resulted in the partial melting of deeply buried rocks of the Asian crust in the Miocene (21-16 million years ago) and the resulting granitic magmas have intruded the upper levels of the crust as dikes and sills. These melt channels also coalesce to form plutons and batholiths. Granitic intrusions of Miocene age which formed as crustal melts differ in their composition from the older Ladakh batholith which has a mixed mantle and crustal origin. There is a lot of interesting and complicated geology in the Trans Himalaya too!
There are lots of technical papers on this topic. For good popular style book I recommend Mike Searle's Colliding Continents: A Geological Exploration of the Himalaya, Karakoram and Tibet.
If you want a short answer to the question I posed, it is this: The Himalaya (including the Tethyan Himalaya) is the deformed northern edge of the India Plate. The Trans Himalaya is the deformed southern edge of the Asian Plate.