Removal beats cleaning because mold roots (hyphae) grow into porous material. Wiping or bleaching the surface leaves the root structure behind, and the colony returns within days. On non-porous surfaces like tile or metal, a small fresh spot can sometimes be cleaned instead.
Containment is what keeps a small problem from becoming a whole-house problem. Disturbing mold without sealing the area sends spores through the rest of the home, which is why professionals build containment and run negative-air HEPA scrubbers before they touch it.
The last and most important step is moisture. Black mold means water has been present; unless the leak, humidity, or drainage issue is fixed, new mold grows on the new materials. IICRC S500 drying and verification is what makes the fix permanent.