Biologists would use the Latin names, so I doubt that would help you any. English having separate words probably comes from America being one of very few countries with both animals.
Not necessarily. The Japanese also have only one word for these two: "wani".
Also I am Hungarian, and we use "krokodil" in everyday life. We do have the word "aligátor" but if you ask an average Hungarian they would say those two words are synonyms. As we only see these animals in the zoo, no-one really notices if they differ somewhat. Of course in those countries where you can run into these reptiles in the wild, you would pay more attention and give them a different name.