The two sides of the same coin are different but stems from the same origin. A double-edged sword hurts both ways! The two expressions mean very different things.

I agree with Ben, and to add to his answer, here is a webpage which explains the meaning of "double-edged sword". Your second saying is not a standard saying in the UK nor, as far as I know, in other English-speaking countries (though other teachers can clarify). However, I can imagine that some languages have this saying and that it has the same meaning as "two sides of the same coin."

It is important to understand the following: 1. The idiom is "two sides of the same coin". This is the correct way to say it. 2. Its meaning is often misunderstood. Here is the definition from the Cambridge Advanced Learner's Dictionary: "If two things are two ​sides of the same ​coin, they are very ​closely ​related ​although they ​seem different." Example: Violent ​behaviour and ​deep ​insecurity are often two ​sides of the same ​coin.