The act of formally requesting or applying for something
When to use
University admission application, Visa application, Contest participation application
The nuance
Used when formally requesting or applying for a service, qualification, or item.
신청 (sin-cheong, sincheong) · 심사 (sim-sa, simsa) · 승인 (seung-in, seungin)
신청 is the act of requesting, 심사 is the evaluation of that request, and 승인 is the final approval.

One lane per word — no nested boxes, just the gist.
The act of formally requesting or applying for something
When to use
University admission application, Visa application, Contest participation application
The nuance
Used when formally requesting or applying for a service, qualification, or item.
The process of evaluating or reviewing submitted applications, materials, or actions
When to use
Thesis review, Contest judging, Interview evaluation
The nuance
Used when reviewing and judging whether an application or materials are appropriate.
The final authorization or recognition after evaluation
When to use
Business plan approval, Building permit approval, Account creation approval
The nuance
Used when officially granting permission after evaluation.
대학에 입학을 신청했어요.
dae-hak-e ip-hak-eul sin-cheong-haess-eo-yo., dae hak e ip hak eul sin cheong haess eo yo.
신청 fits the act of formally requesting admission.
대학 입학을 심사했어요.
dae-hak ip-hak-eul sim-sa-haess-eo-yo., dae hak ip hak eul sim sa haess eo yo.
Admission is applied for, and 심사 evaluates the application; '심사하다' should refer to the application, not '입학' itself.
비자 신청서를 심사 중입니다.
bi-ja sin-cheong-seo-reul sim-sa jung-ip-ni-da., bi ja sin cheong seo reul sim sa jung ip ni da.
Evaluating an application form is correctly expressed with 심사.
비자 승인을 신청했어요.
bi-ja seung-in-eul sin-cheong-haess-eo-yo., bi ja seung in eul sin cheong haess eo yo.
승인 is the approval itself, not something to apply for.
공모전 참가 신청을 했어요.
gong-mo-jeon cham-ga sin-cheong-eul haess-eo-yo., gong mo jeon cham ga sin cheong eul haess eo yo.
신청 correctly describes formally applying to participate.
공모전 참가를 승인했어요.
gong-mo-jeon cham-ga-reul seung-in-haess-eo-yo., gong mo jeon cham ga reul seung in haess eo yo.
승인 applies to permission after evaluation, not directly to participation.
논문 심사 결과가 나왔어요.
non-mun sim-sa gyeol-gwa-ga na-wass-eo-yo., non mun sim sa gyeol gwa ga na wass eo yo.
심사 refers to the evaluation process of the thesis.
논문 승인을 받았어요.
non-mun seung-in-eul bat-ass-eo-yo., non mun seung in eul bat ass eo yo.
승인 means the official acceptance after evaluation.
Which sentence best uses '신청'?
When is '심사' appropriate?
Which sentence correctly uses '승인'?