1. A(어/아)서 B 하다: Do B "by" doing A. In this case, A is the way to do B and what is happening during B ex1) 걸어서 올라가다 You climb by walking. You keep walking during climbing ex2) 헤엄쳐서 건너다 You go there by swimming. You keep swimming during going there ex3) 차를 몰아서 올라가다 You climb by driving a car. You keep driving during climbing. 2. A(아/어)고 B하다: Do B "after" doing A: In this case, B happens after A. ex4) 차를 타고 올라가다 You climb after you ride a car ex5) 차를 타서 올라간다 (unnatural) 3. Only in the cast of the meaning above, the reason seems clear, but in general the usage -(아/어)서 -(아/어)고 is more complicated. There is different usage, because -고, -서 includes other meanings. ex5) 차몰고 간다(o), 차몰아서 간다(less common) You go by driving a car ex6) 책보고 공부한다 (o), 책봐서 공부한다(unnatural) You study by reading.

First, I'd like to say it's a great question. ~서 means : by ~ 걸어서: by walk (on foot, in smooth English) 차를 타고: by car Actually, there's "서" which is omitted in the sentence. The original form is "차를 타고(서 )". However, for so many years, "some transportation + 타고 (ride something)" has been used a lot and became a standard form. So, we use "차를 타고", but the meaning is the same as "차를 타고서." Whey you see this kind of grammatical variance, please don't stick too much. It's not something you can catch up within few days. Although you may not be able to get all the grammars, there's no problem to communicate. Just try to get used to it and use Korean more. Hope it helps :)