1. They are idioms, not proverbs. 2. They have different meanings: The idiom "kill two birds with one stone" is about jobs that need to be done. It refers to an action which achieves two goals at the same time, thereby saving you the time and trouble of doing two jobs. For example, if my two aims for this morning are buying some books and giving my dog some exercise, I could take my dog on a walk to the bookshop - this kills two birds with one stone. One trip = two things achieved. The idiom the "the best of both worlds" refers to a solution which gives you the advantages of two different situations and none of the disadvantages. Let's say that you can't decide whether to live in the city or the countryside. Then you see a house in a quiet suburb with lots of greenery, but which has fast transport connections into the city centre. Living in this house gives you the best of both worlds - the advantages of both options ( a pleasant environment and easy access to the city centre) and none of the disadvantages (such as the noise and dirt of the city or the isolation of the countryside). I hope that makes sense.

No, they do not mean the same thing. To kill two birds with one stone, means to achieve two objectives with one action (e.g., by reading A brief History of England, you've both practiced your English reading skills and you've brushed up on your English history). To have the best of both worlds, means to have the advantages of two things that were somehow thought to be mutually exclusive (or at least were thought be quite distinct from one another). So let's say you're using a language textbook that combines modern and traditional pedagogical approaches, if the textbook is able to extract what's really good from each method, you can say it has the best of both worlds.

Hello Marzi, no, you can't use them interchangeably because they have different meanings. "To kill two birds with one stone." means to accomplish two different things with one action. "To have the best of both worlds." means to be able to enjoy the best of two different situations or environments at the same time. Here are a couple example sentences: "I'll kill two birds with one stone by getting gas and dinner when I go out." "He has the best of both worlds by living at home while going to school because he can enjoy living without rent while participating in all the school has to offer." Hope that helps!