So in Korean this has to be written as two sentences, and can't be chained together like this one?
It can be written as 이 남자가 뚱뚱하고 저 남자는 날씬합니다 without any problem. Basically when you write two separate sentences, you use 그리고. When a single sentence, you use ~고 ending
Notice the usage of 는 in the second clause. It is used because of the contrast in fat vs skinny between the two men.
Tag yourself I'm the thicc man (Duolingo can apparently change my gender just like that. Interesting.)