辍学 means to discontinue one's study halfway. 退学 just means discontinuing.

辍学 to be not able studying.as family has a bad situation. 退学 be stopped studying by school , as do something wrong or be not abidance by the rules of the school.

Good to know that there's another subtle distinction! Thanks!

As far as I remember from school, 退学 is mostly used when the school expels you, rather than you 辍学 drop out yourself

"辍学"implies a student voluntarily withdraws from the course of study; in contrary, "退学" is used when a student was terminated or expelled by the institution.