I am unsure if Haalkitaine uses those terms in the same manner.
For example, a "Duchy" was usually a a sub-section of a kingdom (albeit often with a fair amount of 'independance') while a "Grand Duchy" was usually independant and sovereign; i.e. not part of a larger kingdom.
But even those 'definitions' were not hard and fast.
For example, [currently] the Duchy of Normandy (an inherited title) consists only of the Channel Islands (a mere fraction the size of the Duchy at its height).
Also, a 'riding' was (generally) a third of a county (compare to farthing - which in some uses meant a fourth of a county) but even that was not a 'hard and fast' rule.
And, FWIW, the [Earth] origin of this use of the word riding is not based upon "everything within a day's ride" [on horseback].
I'll have to check my copy of Haalkitaine when I get home.
DonMoody