Both forms perform initialization. The first syntax (with ()) is called direct-initialization syntax. The second syntax (with =) is called copy-initialization syntax. They will act same in most real-life cases, but there are indeed differences between the two.
In situations when types on the left-hand side (LHS) and right-hand side (RHS) are identical (ignoring any const/volatile qualifiers), both are indeed exactly the same. The language standard explicitly states that in this case the = form is equivalent to () form.
But when the types are different (and the LHS type is a class type), these two forms will generally work differently.
- The copy-initialization form works as follows: convert the RHS value to the temporary object of LHS type (by any means possible: standard conversion, conversion operator, conversion constructor). And then use the copy constructor of the LHS class to copy the temporary object to the LHS object. 
- The direct initialization form work as follows: just consider all constructors of LHS and choose the most appropriate one by using overload resolution. 
You can immediately notice that the copy-initialization syntax unconditionally uses the copy constructor (the copying and the intermediate temporary can be optimized away, but conceptually they are there). If the LHS class has no accessible copy-constructor, the copy-initialization unconditionally becomes ill-formed, while direct-initialization might still work. 
Also, the keyword explicit applied to certain constructor will affect which form of initialization is available for which combinations of types.