Here's a full description including both cases you mentioned. There are four sentence ending forms that are widely used, which differ only in formality and politeness. 1. -(ㅂ/습)니다 - formal and polite (as in public addressing, talking to a senior person) 2. -(ㄴ/는)다 - impersonal, informal (most written articles and novels use this style) 3. -아/어요 - polite (most common and preferred form between adults) 4. -아/어 - informal (between close friends and when addressing children) Examples of 가다, 오다, 하다, and 먹다. 1. 갑니다, 옵니다, 합니다, 먹습니다. 2. 간다, 온다, 한다, 먹는다. 3. 가요, 와요, 해요, 먹어요. 4. 가, 와, 해, 먹어. For (1) and (2), consonant-ending stems (e.g. 먹다) conjugate with the full syllable 습(먹습니다) and 는(먹는다), while vowel-ending ones take a ㅂ(갑니다) and ㄴ(간다) respectively. For adjectives, the -다 ending (2) conjugates differently. Adjectives do not take the additional ㄴ or 는 because they represent a state instead of an action. Examples of adjectives 좋다(good) and 슬프다(sad). 1. 좋습니다, 슬픕니다. 2. 좋다, 슬프다 (not 좋는다 or 슬픈다) 3. 좋아요, 슬퍼요. 4. 좋아, 슬퍼. Lastly, there are two important special cases 이다(is) and 아니다(is not). 1. 입니다, 이다, 이에요/예요 (학생이에요, 학교예요), 이야/야(학생이야, 학교야), 2. 아닙니다, 아니다, 아니에요, 아니야.

Thank you so much for your answer.

V-ㄴ다/는다 : declarative form (present) (used for news, writings, presentations, or diary entries) 아요, 어요 and 해요 are present tense