buy a/the round (of drinks)
To buy drinks for each person in a group. "Next" is commonly used before "round" (when "the" is the article). If your new friend is buying us a round of drinks, then I like him already! OK, who's buying the next round?
buy a round (of drinks)
and buy the next round (of drinks)to buy a drink for each person present, with the expectation that one or more of those persons will later do likewise. Which one of you guys is going to buy the next round?