For example, sometimes when people say a joke (=jest), they later denote that "it's just a joke" so they can say "It's just a jest"?
Jests and jokes are frequently interchangeable when they refer to language - what people have said or written rather than to actions. (Note that it's idiomatic to tell a joke or play a joke on and to speak in jest.)
Jests are also described as playful banter, droll tales - although their meaning has evolved over time.
They once signified an act intended to amuse and could also refer to a person being ridiculed; these senses of the word are archaic.
From jest we get a jester, a figure both of fun and subtle influence, whose role was to entertain the court and is an important figure in some historic plays.
Unlike jest today, the word joke can be used in other contexts.
You can play a joke on someone, a prank (whereby you surprise and hopefully amuse them)
and you can call someone a joke, meaning that they are worthless, incompetent to hold office or do a job.
In the context you refer to, the words mean the same thing.