>>17754250
The former is a stand-in for the kings subjects whose job is to predict all touchy talking points that he may encounter, whereas all the other are deliberately chasing laughs and applause from those subjects. The conflation of Jesters being clowns is due to clowns' humorous imitations of Jesters and what the populace dreams that the conversation between the Jester and the King might look like.
tldr;
The Jester is the semantic vice-king,- the Loki to the kings Odin. His job is to present all variants of disaster to the king so that time can be to his advantage.