The topmost image is a Classical-Age Greek vessel known as The Douris Cup, now housed at the Vatican and portraying what is by now a nonstandard version of the Jason and the Golden Fleece story. In this version it seems the sea-serpent (dragon) Ladon swallows down Jason but coughs him up again, rather as if a re-telling of the story of Jonah and the Whale. The creature is in fact often called a 'whale' or Ketos, which is used mostly in the generic sense of 'Sea Monster'
In this case the creature has a definitive and definite marker of a Plesiosaur, the opening in the skull behind the eye called the Euryapsid skull type and at one time used as the hallmark of that entire division of reptiles (classification is currently disputed and the trait is not seen as anything, which means the various other animals formerly classified together with Plesiosaurs are not now seen as actually close relatives).
Snakes have nothing like this. In fact snake skulls are more nearly a latticework of bony rods and nothing like so solid a skull.
Here is another view of another Ketos from a Roman Marine mosaic. The type of creatures are often shown as strangely long-necked quadrupeds but sometimes only the front limbs are shown. 'Sea horses' are a slight variant and they are sometimes directly called 'sea serpents.' (Of the long-necker variety).Below is a skeleton of the Plesiosaur Cryptoclidus for comparison. Plesiosaur images are from the invaluable internet resource, Oceans of Kansas.
http://www.oceansofkansas.com/plesiosaur.html
