There are many ancient orders and organisations that have survived to the present day. The Knightly Orders are listed apart from the state. The members are bound by law to answer the call of the monarchy in times of war, and they own and rule land at the sufferance of the ruler but the organisations themselves are not state run.
The nobility enjoy extra rights and responsibilities over the common man. They can issue challenges to other aristocrats on matters of personal honour. They enjoy a standing in court and a stronger legal position (they cannot be accused of a crime without proof, whereas a commoner accused by a noble is often arrested whilst the investigation is conducted then acquitted later if evidence is not available). They can own land in large quantities and they are allowed to raise a personal army. All this is at the sufferance of the monarch and frequently the benefits are a double edged sword. Being drawn into court means getting involved in court politics. Being immune to insubstantial accusations makes the dagger in the dark a more tempting way of removing ones enemies. Having an army is a considerable expense to fund something of which the crown often makes use.
All knights are members of the nobility and enjoy the rights and responsibilities hither thereto. The path of the knight often begins young when the hopeful becomes a page in the service of an existing knight. From there he rises to become a squire, who is either attached to knight or sometimes sent into the realm on tasks himself. Eventually he rises to the rank of full Knight of the Realm and is given the honorific Sir. Knights of various ranks often join one of the Orders.
All knights are nobles because to be a knight is to be a noble. The monarch sometimes knights an individual, giving him the rank of squire or even full knight and those individuals are henceforth legally considered to be a noble.
State Organisations are directly under the control of the government and ultimately the reigning monarch.