Official tasks or projects assigned at school or workplace
When to use
official school tasks, workplace tasks, research projects
The nuance
Use 과제 for official, broad tasks or projects, both in school and workplace contexts.
과제 (gwa-je, gwaje) · 숙제 (suk-je, sukje)
과제 refers to formal tasks assigned at school or work, while 숙제 mainly means homework students do at home.

One lane per word — no nested boxes, just the gist.
Official tasks or projects assigned at school or workplace
When to use
official school tasks, workplace tasks, research projects
The nuance
Use 과제 for official, broad tasks or projects, both in school and workplace contexts.
Homework mainly done by students at home related to school studies
When to use
student home study, school study tasks, homework for K-12 students
The nuance
Use 숙제 only for study-related tasks students do at home, directly linked to schoolwork.
이번 과제는 회사에서 제출해야 해.
i-beon gwa-je-neun hoe-sa-e-seo je-chul-hae-ya hae., i beon gwa je neun hoe sa e seo je chul hae ya hae.
Refers to workplace task, so 과제 is correct.
이번 숙제는 회사에서 제출해야 해.
i-beon suk-je-neun hoe-sa-e-seo je-chul-hae-ya hae., i beon suk je neun hoe sa e seo je chul hae ya hae.
숙제 is for school study tasks, not workplace tasks.
선생님이 숙제를 내주셨어요.
seon-saeng-nim-i suk-je-reul nae-ju-syeoss-eo-yo., seon saeng nim i suk je reul nae ju syeoss eo yo.
Homework assigned by teacher for home study, so 숙제 fits.
선생님이 과제를 내주셨어요.
seon-saeng-nim-i gwa-je-reul nae-ju-syeoss-eo-yo., seon saeng nim i gwa je reul nae ju syeoss eo yo.
과제 can be used for official school assignments or projects.
나는 숙제를 회사에 제출했어요.
na-neun suk-je-reul hoe-sa-e je-chul-haess-eo-yo., na neun suk je reul hoe sa e je chul haess eo yo.
숙제 is for school homework, not for submission at work.
나는 과제를 집에서 했어요.
na-neun gwa-je-reul jip-e-seo haess-eo-yo., na neun gwa je reul jip e seo haess eo yo.
과제 can be done at home if official task, so correct.
학생들은 매일 과제를 해야 한다.
hak-saeng-deul-eun mae-il gwa-je-reul hae-ya han-da., hak saeng deul eun mae il gwa je reul hae ya han da.
과제 can mean official study tasks assigned at school.
학생들은 매일 숙제를 해야 한다.
hak-saeng-deul-eun mae-il suk-je-reul hae-ya han-da., hak saeng deul eun mae il suk je reul hae ya han da.
숙제 is natural for daily homework students do at home.
Which word fits workplace tasks?
What is homework done by students at home?
Official research project assigned at school?
Which is study-related homework given at school to do at home?
What does it mean?