Plumber Snake
The Plumber Snake is a situation where one person is giving another person a blowjob and the recipient begins to vomit as the giver is ejaculating in the other's mouth.
You surely may come upon videos that demonstrate the concept behind the definition of the Plumber Snake.
Plumber's Snake
A coiling shit that resembles a snake with one end extending down through the toilette.
This plumber's snake isn't going to unclog anything!