I'd rather other people gave their own impressions, but as the writer I guess I should give my own input.
Yes, there are distinct provinces. The governmental system works like this: there is one regime sheet, on which the statistics and type of government are detailed, and one or more province sheets that are retained by the DM, detailing the inherent resources, factions and so on that are found in the province.
Provinces are not fixed, inasmuch as there is no hard and fast rule to say that a province must be of such-and-such dimensions. This was deliberate on my part. What I wanted to create was a system whereby existing maps and campaign settings could easily be adapted across into the S&D mechanics. S&D uses set formulas to calculate such things as resource yield, population growth, tax revenue, available solidery and so on, based on the data that already exists in the campaign. The only real limit on a province is the number of different types of resource that it can produce.
Essentially, you can divide up an existent campaign map into one or more provinces according to what will make for the most convenient management. It can be as intricate or as straightforward as the DM wants to make it. When I put the system together, I envisioned provinces as fairly large; you could certainly have a single kingdom with only one province.
The really important distinction between one province and the next is political. Each province has a faction section in which the standings of the three tiers of society - nobles, merchants and workers - along with any other factions are detailed. The governing actions you take in the province affect the whole region and thus affect how each of the tiers of society therein thinks of your regime. So, if you tax the peasants of one province and use the proceeds to feed the peasants of another province, the former will be angry while the latter will be grateful.