As of this writing, we believe the sea he originally imagined actually did exist late in the Miocene period (20 Ma), but had a long and interesting history behind it. In the late Jurassic (150 Ma) and Laurasia and Gondwanaland began to splinter into masses resembling the continents we see today - Africa began turning counter-clockwise and India sped northeastward over the eastern end of the Tethys Ocean. As that part of the Tethys Ocean disappeared under Cimmeria, the relatively shallow area in the western end of the Tethys Ocean opened onto the growing Atlantic Ocean, forming the Tethys Seaway or Tethys Sea. Over the next 120 million years, even the Tethys Sea would shrink, closed in an all sides by Africa, Saudi Arabia and Europe, eventually becoming Mediterranean, Black, Caspian and Aral Seas.
Like every science, geology is a continuously evolving system of theories, and the terms used to describe various pre-historic formations have fluctuated as more accurate theories have emerged. But terms in previously published works don't always match up with the new terms. Many sources use "Tethys Ocean" to refer to the "Tethys Sea" and vice versa. Some even refer to the growing Atlantic Ocean during Jurassic as the Tethys Sea, so be sure to double check which entity is being referred to in a particular situation.