Which one is for visas and which one is for study
KIIP (사회통합프로그램, Korea Immigration & Integration Program) is the Ministry of Justice's free language and culture course for foreign residents. It has stages 0 to 5 (0–4 are Korean language, 5 is Understanding Korean Society), each ending in a test. Unlike TOPIK it is a course-plus-test programme, not an exam, and only residents of Korea can take it.
Study (D-2, D-4 visas), scholarships (GKS), skilled work (E-7) — TOPIK. Universities do not accept KIIP as proof of language ability.
Changing visa and settling: F-2-7 points visa, F-5 permanent residency, F-6 marriage visa, naturalisation (귀화) — KIIP is the stronger option. Completing KIIP stage 5 exempts you from the naturalisation language test and adds points for F-5/F-2. TOPIK also earns points, but KIIP FULLY satisfies some requirements.
A TOPIK certificate exempts you from the KIIP placement test (사전평가) and places you directly into a higher stage: TOPIK 1 → stage 2, TOPIK 2 → stage 3, TOPIK 3 → stage 4, TOPIK 4–6 → stage 5 (one stage above the level you have already proven). The mapping is maintained in the Ministry of Justice notice — check socinet.go.kr. In other words, getting TOPIK 4 first and then joining KIIP skips all 400 hours of the language stages.
Not yet in Korea, or planning to study or apply for a scholarship — TOPIK, there is no alternative. Living in Korea on a work or family visa and planning to stay long-term — KIIP, because it is free and more effective for visa points. The two are not mutually exclusive: most people get TOPIK 3–4 first (for work and settling in), then go for F-5 or citizenship with KIIP 5.