Gents,
IMTU, the term 'Pocket Empire' refers to a *multi-system* polity which may or may not be politically aligned with any of the 'Big Five'; the Zhodani Consulate, Third Imperium, Solomani Confederation, Hive Federation, and 2000 Worlds. (The fractious nature of Aslan and Vargr societies preclude any idea of a unitary state within those regions of Charted Space they control. Most Aslan and Vargr polities are 'pocket empires'. Some may even be aligned with one of the 'Big Five' and are therefore 'client states'.)
'Client State' refers specifically to any polity that is aligned with a larger entity, regardless of size. A client state can be a pocket empire, a single system, or a single nation on a balkanized world.
The Darrian Confederation, Sword Worlds Confederation, Border Worlds Confederation, and Federation of Arden are all pocket empires. Of the four, only Arden is not a client state.
Thus, 'pocket empire' is an astrographic description and 'client state' is a political description. The two labels are not mutually exclusive.
Sincerely,
Larsen