The forms such as 먹다, 가다, etc. are called 동사원형(the original/simple form of verb), that has no tense and no conjugation. The present tense of verb is made by attaching "ㄴ" or "는" to verb's stem, like these. 먹-는-다, 먹는다 when the last syllable of stem has 받침, like 먹(ㅁ-ㅓ-ㄱ), '는' is used. 가-ㄴ-다, 간다. when the last syllable of stem has no 받침, like 가(ㄱ-ㅏ-x), 'ㄴ' is used and combined with stem. 먹어요 and 가요 are conjugated forms by "-어/아/여요", a speech level ending of "해요체". 먹-어-요, 먹-어요 가-아(leaving out)-요. 가-요 declarative sentences of six speech level ending (present tense form) original form, 먹다, 가다 합쇼체: 먹-습니다. 갑니다. 해요체: 먹-어요, 가-요. 하오체: 먹-으오, 가-오 하게체: 먹-네, 가-네 해체: 먹-어, 가 해라체: 먹-는다, 간-다.

The first form is a polite conversational form, used for speaking. The second is a narrative form, used fot writing.