Broma
Una broma: a joke (noun)
Bromear: to joke, to kid
Estar de broma: to be joking, to be joking around
Gastar una broma: to play a joke
Aceptar una broma: to take a joke
Broma habitual: running joke

Chiste
Un Chiste: a joke (noun) Chiste can often be used interchangeably with broma.
Hacer un chiste: to make a joke
Contar un chiste: to tell a joke
Mandarse un chiste: to crack a joke

Burlar: to joke, to make fun of
una Burla: a prank, practical joke
un Burlón: a jokester, someone who is always kidding around. This word can also mean “bully”