Honorary and Equivalent Ranks
The 'Equivalent Ranks' system is designed to let those in the army and out of it know who holds comparative ranks to whom. Allies who do not wish to be beholden to Amber may hold honorary ranks in the Army or Navy, without prejudice to their independence. In general, 'Honorary' means little responsibility, and no authority, while 'Equivalent' means that there is some mutual respect due.
Outside the Central Structure
One of the reasons that the Amber army is so loose in titles and such is that it is literally a patchwork. You can buy yourself commissions up to Lt-Col in existing units… but if you muster your own men, that defines your station/rank within your own army. Muster 1000 soldiers, you can call yourself a Colonel or Knight Commander or whatever legally proper title you wish. Muster upwards of 5000? Brigadier if you want. 20,000? Major General territory. However, you cannot buy the title in the Army itself.
Instead, you will probably be awarded an equivalent rank depending on your status. It is possible to hold a real and an equivalent rank, but the practice is frowned on.
A feudal army that is attached to a professional core will have many unique points. The distinction between 'real' and equivalent titles blurs in places. While an Honorary Colonel may do nothing but review troops and present prizes on competition days, a Mandate-Colonel can command regiments in battle.