Both 하고 (actually just -고) and 그리고 mean "and". The difference is that 그리고 is much heavier in nuance and length. 그리고 comes from 그리하고 which is a short form of "그렇게 하고", or "그렇다(고) 하고". 그렇게 하고 is like "with that done, ...", and 그렇다 하고 " with that said, ...". What really distinguishes the two are their usages however. -고 is short, light, and convenient, so it is used much more widely. 그리고 is longer, more emphatic, and can be used in the beginning of a sentence unlike -고. You can look at some examples. 1) 밥을 먹고 학교에 가자. Let's eat and go to school. 2) 밥을 먹자, 그리고 학교에 가자. In #1 "밥을 먹자" and "학교에 가자" are connected without even adding one syllable. So it is very efficient and used all over the place in the language. #2 is preferred if you want to say it slowly, draw extra attention, and the like. Another distinct difference is when "and" is used in the beginning. Ex: "And then there was you" 1) It is not possible to use -고 since it requires a preceding verb. 2) 그리고 네가 있었다. So, for the relatively short "and" in English, Korean has the even shorter -고 and the much longer 그리고. "but" is also very similar, with -만 and 그렇지만/하지만. 그렇지만 comes from "그렇게 하지만", "그렇다(고) 하지만" (that is so, yet...). Examples. "He is tall but can't play baseball." 1) 그는 키가 크지만 농구를 못한다. 2) 그는 키가 크다, 그렇지만/하지만 농구를 못한다. "Everything worked out. But then a problem came up." 1) not possible to make two sentences using -만 2) 다 잘 되었다. 그러나 문제가 하나 생겼다.