The ㄱ sound is not exactly the same as k or g. As an approximate description, we say it's like k when it's at the beginning of a word, and g otherwise. The reason is because when ㄱ comes after another (vowel-ending) syllable, as in 자기야, it loses its sharpness and degenerates to a g-like sound because of the smoothing effect. It's because we tend to put more emphasis on the beginnings of sentences and words. It's still not quite the same as g but close enough for practical purposes, especially when spoken fast (but if the preceding syllable ends with a consonant, as in 국가, it can take on a different sound depending on the type of the consonant). ㄱ at the beginning of a word sounds closer to k than g (it is an "unvoiced" consonant), except that there is no strong aspiration and that the overall sound is duller and heavier because it is pronounced further back in the mouth than k. ㅋ is closer to k than ㄱ.

We pronounce ㄱ like g and ㅋ like k.