Hello!
The similarity between "Blue Danube" and "Skating Waltz" is that they are both very beautiful waltz styles. They are all composed of several small waltzes, and the transitions between sections are natural and rigorous.
However, "The Blue Danube" was written by the Austrian Johann Strauss, and "Skating Waltz" was written by the French composer Walder Teifer.
In fact, the melody is still different. You will naturally find it when you become familiar with it. "Blue Danube" has a more royal and purely classical atmosphere, while "Skating Waltz" is full of romantic and classical atmosphere.