The Statue of Liberty in NY is officially named 'Liberty Enlightening the World' while the Statue of Freedom in DC was originally called 'Freedom Triumphant in War and Peace' and known by many as 'Armed Freedom.' She stands on top of the Capitol Dome. She looks very different from her sister in NY, holding a sheathed sword in her right hand and a shield and laurel in her left hand. Inside the Dome, Freedom can be seen in a fresco.
Here is an interesting tidbit on the Statue of Freedom. The designer originally intended for Freedom to wear a Phrygian cap, otherwise known as a liberty cap. This hat was the symbol of a freed Roman slave. The Senator in charge of the Capitol construction projects - Jefferson Davis (yes, he was later the President of the Confederacy) - did not like the idea of the cap and asked that it be replaced with a helmet. And so, Freedom wears an eagle helmet. The Statue of Freedom was placed on top the Capitol Building in the midst of the Civil War in December of 1863.