The Orange-Nassaus and Nassaus are obvioiusly related because look at thier names. The short version is that they are all directly descended from Walram, Count of Nassau who died in 1198.
They split into two branches the elder branch Nassau-Wielburg (Luxembourg) and younger branch Nassau-Dillenburg (later Orange-Nassau).
Orange
Henry III Count of Nassau-Breda, a descendant of Walram, married Claudia of Chalons and Orange. She was an heiress and the son Renatus became Prince of Orange and later bequethed all of it to his 1st cousin William the Silent in 1545. He later went to the Netherlands and became Stadholder of the Netherlands showing himself a natural leader.
*sidenote his daughter Louise Juliana married Frederick IV Elector Palatine who was great-grandfather of George I king of Great Britian and Ireland.
Anway later on the heir of William III, Prince of Orange, King of Great Britian in the Netherlands, William IV, his twice cousin-removed, had a son a daughter. the son became William V and the daughter married Karl Christian Duke of Nassau-Weilburg the great-grandfather of Adolph the 1st independent Grand Duke of Luxemburg.
Also Tsar Paul I's second wife Sophia of Wurtemburg was sister to GD Adolph's father Wilhelm's bro-in-law Duke Louis who married his sis Henrietta in 1797. Paul and Sophia's daughter Anne married Willem II king of the netherlands, so I guess that's how they connect.
Plus Anne's nephew by her brother Nicholas I married Alexandra of Oldenburg who was the daughter of Peter Duke of Oldenburg who married Theresa of Nassau sister of GD Adoplh.
Don't you love how they connect? That's why I'm obsessed.