Jefe vs. chef
While the words jefe and chef might sound similar and both relate to being in charge, they are used in very different contexts in Spanish. Jefe is a general term for any boss, while chef is a very specific term for a culinary professional.
Jefe
A2Jefe (or jefa for a female) is the standard and universal Spanish word for boss, chief, leader, or head. It is a broad term used in any professional, organizational, or even informal setting to refer to the person in charge.
Mi jefa me pidió que terminara el informe para mañana.
(My boss asked me to finish the report for tomorrow.)
Él es el jefe del departamento de recursos humanos.
(He is the head of the human resources department.)
En este proyecto, María es la jefa del equipo.
(In this project, María is the team leader.)
Un buen jefe debe saber cómo motivar a sus empleados.
(A good leader must know how to motivate their employees.)
Le pregunté al jefe de obra cuándo estaría terminada la casa.
(I asked the site foreman when the house would be finished.)
Coloquialmente, algunas personas llaman 'jefe' o 'jefa' a sus padres.
(Colloquially, some people call their parents boss.)
Chef
B1Chef is a loanword from French used specifically to refer to a professional cook, particularly the head cook who directs the staff in a restaurant's kitchen. Its use is restricted to the world of gastronomy.
El chef preparó un plato exquisito con ingredientes locales.
(The chef prepared an exquisite dish with local ingredients.)
Ella estudió en París para convertirse en una chef de alta cocina.
(She studied in Paris to become a haute cuisine chef.)
El restaurante es famoso por su innovador chef ejecutivo.
(The restaurant is famous for its innovative executive chef.)
El programa de televisión busca al mejor nuevo chef del país.
(The television show is searching for the country's best new chef.)
Mi hermano sueña con ser un chef y abrir su propio restaurante.
(My brother dreams of being a chef and opening his own restaurant.)
Summary
In essence, the key difference is specificity. Every chef is the jefe of their kitchen, but a jefe is not necessarily a chef. Use jefe for any kind of boss or leader in any field (business, construction, projects) and use chef exclusively for a professional head cook in a culinary setting.