A noble house is an aristocratic family or kinship group, within the Empire.
That is either currently or historically of national or international significance, and usually associated with one or more hereditary titles like the most senior of which will be held by the "Head of the House" or patriarch/Matriarch.
A noble house holds influence and political power within the internal structure of the Empire and are mostly located in the main cities and the Capital being the heart of the nobility's dealings.

Many noble houses have birthed dynasties and have historically been considered royal houses, but in a contemporary sense, these houses may lose this status when the dynasty ends and their familial relationship with the position of power is superseded. A royal house is a type of noble house, and they are not separate or mutually exclusive entities.

A power base refers to, as stated, a base of power.
Powerbase can be anything that provides oneself with tools for more power.

They are most often composed of subservient actors who willingly serve and carry out tasks for their superior. Their presence grants an 'external power' in the form of influence, and an 'internal power' in the form of stability. They make it easier for someone to do things, and harder for others to do things to them.

It can be a network or resources that serve to provide one with factories, armies, estates and droids but also powerful contacts.

A power base holds authority that is often based upon the size and influence of the powerbase itself.