Why to use empty parentheses in Scala if we can just use no parentheses to define a function which does not need any arguments?

As far as I understand, in Scala we can define a function with no parameters either by using empty parentheses after its name, or no parentheses at all, and these two definitions are not synonyms. What is the purpose of distinguishing these 2 syntaxes and when should I better use one instead of another?

It's mostly a question of convention. Methods with empty parameter lists are, by convention, evaluated for their side-effects. Methods without parameters are assumed to be side-effect free. That's the convention.

Scala Style Guide says to omit parentheses only when the method being called has no side-effects: http://docs.scala-lang.org/style/method-invocation.html