It seems almost no one has taken into account one very important thing that they are two different verbs: 끓다 - to boil (water boils (by itself) - 물이 끓어요) and 끓이다 - to boil something i.e. stew (저는 김지찌게를 끓여요)...of course I am not an expert nither English nor Korean sa I can be wrong....
Good point. This is the case of a causative verb 끓이다 derived from a passive verb 끓다.
• 끓다 = come to the boil = boil [intrans] = be boiling, where boiling is a gerund describing an ongoing state.
끓는 물 = water at boiling point
• 끓이다 - bring (something) to the boil = boil [transitive] = be boiling (something), where boiling is a present participle describing a process
끓이는 물 = water being brought to the boil