Because I don't want to write about it without it actually being desired, would you like an explanation of how the provinces were governed during early Byzantine times? It's quite similar to the later Empire (although the non-important distinction between senatorial and imperial provinces is gone by then), and I can also describe the Theme system.

Imperial provinces had their governors appointed directly by the princeps and Senatorial provinces appointed promagistrates of their own, according to the procedures that had been put in place by Sulla and that derived from much older legislation. That's the crux of it, although it's more nuanced of course. In 27 Augustus was given an extraordinary consular province as part of his imperium maius, consisting of Spain, Gaul, and Syria (with more provinces probably added later). These provinces he governed by proxy, by appointing legati pro praetore (who held imperium, though due to Augustus' imperium maius this was subordinated to the *imperium of the princeps) and entrusting the finances to procurators. These propraetorian legates were of the senatorial class and were of consular rank, but were very much subordinate to the princeps and his imperium. The procurators were normally equites, like the prefects (like Pontius Pilate) that governed minor Imperial provinces like Judaea or Thrace. With the exception of Africa, which contained one legion, all legions were permanently stationed in Imperial provinces governed by a propraetorian legate (usually not those governed by a prefect) and the recruitment of additional legions was heavily policed by the princeps. Senatorial provinces were governed in the old way, with promagistrates (I believe always proconsuls during the Principate--during the Republic praetorians could also be given propraetorian provincial commands, but this seems no longer to have been the case under Augustus) governing the province with the assistance of regular (that is, not propraetorian) legates and quaestors. Proconsular commands in the Senatorial provinces, though, were subject to review by the princeps, who held tribunate power and could therefore veto appointments, although I don't know of this ever actually occurring. Egypt was the exception to all this. Egypt was governed by an equestrian prefect who was allowed to command legions, and it was forbidden for senators to enter the province without permission from the princeps

Ouch. This is a big topic, and I'm not sure if I'm the best person to answer it... Too much Roman law, I just know the stuff with flash and glamour, the gods and battles and sex and orgies and gladiators and stages etc...! I do know the basics, though.

A short overview for Roman West (and, I think, East as well broadly): Administration patterns differed quite a lot across the empire and at different times. In fact, 'administration' might not be even the best word for it, as the majority of political units (ie villages, towns, tribes) under the Empire were autonomous units that retained their local forms of government and laws - this was true long into the high Empire. Their main relationship to the city of Rome was that they paid tribute (either money or produce) and were required to supply troops to the Roman auxiliary forces. These sorts of Roman subject-states or cities were called foederati ('allied states', as ironically the Romans called them). But, there were different classes or statuses that provincial units could have, i.e. municipium, colonia civitas, and all sorts of sub groups of those. The status basically defined, what sorts of privileges and rights the inhabitants had in the wider political network of the empire, whether they had citizenship, did they have Roman laws and Roman style government etc... Basically, foederati were considered the lowest type of provincial unit, and the more 'Roman' structurally the unit was, the higher its status was. The Roman model encouraged the local elite in the provinces to compete for prestige, and to create connections and loyalties to Rome. The Romans rewarded the good boys by giving them more power in their local political spheres, and then let them take care of things quite freely, as long as the tributes were paid in time. This system suited the Romans well, because they didn't have time to look after each little hamlet. And of course, each province had a governor, appointed by the emperor or the senate, who was responsible for keeping peace, tax collecting, drawing troops etc. Holding a governorship was both a prestigious and profitable gig, since they were allowed to exploit the resources of the province of their appointment for their own gain to a degree. Plus the emperor could pay you 1,000 000 secertes a year, mm-mm.

It's of course a lot more complicated and fine tuned than that, but that's roughly the full picture I believe most classicists could give you. If you want, I can try to give a more detailed picture of the everyday running of e.g. the province of Britannia or Hispaniae, which I know best, with a bit more reference to the ancient sources? Although, Britannia is a bit weird in terms of administration in comparison with the other provinces.

I personally don't know much about the Roman East, the only touch stone I have on the administration in there is Younger Pliny's and Trajan's correspondence, so hopefully someone else can pitch in there. I know lot of the terminology at least was different in the Greek-speaking East, but I'm not quite sure if the administration was structurally different.

And, the difference between the two types of provinces. The following is not gonna be very interesting, as one of the main difference was that they had a different make-up of officers that took care of the administration. So, a list of Latin terms! Yay!

The senatorial provinces are the old Republican provinces, which retained the old administrative structures. Usually, the Roman personnel in the provinciae was very limited. Apart from the governor, there was, a quaestor for collecting taxes and paying the military, several legates (legatus) as representatives of the governor, a larger group of relatives, political friends and advisers (cohors amicorum) as well as clerks (scribae), lictors and other subordinate staff.

Then, when Augustus was made emperor in 27 B.C, the Senate assigned almost all of the Roman border provinces to him personally; this is where most of the legions were stationed. From here on, there's a tradition to keep legions mainly only in these imperial provinces, firstly because they are where the borders & unrest tend to be, and secondly, if the legions were kept in the provinces close to Rome, there was the danger that a governor could win the favor of the military and overthrow the emperor. See map. The governors of the senatorial provinces had the rank of proconsul, were chosen by lot and appointed by the Senate for one year. Africa and Asia were administered by former consuls, the other provinces by former praetors.

In the so-called imperial provinces, the emperor appointed a sub-governor of propraetor rank (legati Augusti pro praetore - the emperor was technically the governor of these provinces), whom he recruited from the group of former praetors or consuls, depending on the number of legions in the province in question. The sub-governor usually remained in office for three years, but occasionally also much longer. Some legati iuridici were added in some imperial provinciae to relieve the governor of jurisdictional duties. The taxes in imperial provinciae were administered by procuratores.

But, the difference between the two types of provinces is mainly in that the focus of the balance of power between the senate, the emperor, and the province were different; but, for the provincials themselves, there was not really any difference between the two types. The two categories existed to cater for the interests and ambitions of the emperor and the senate, respectively; the emperor wanted to be able to appoint trusted men to areas where the legions were, but at the same time, the senators wanted to get an equal chance to get a piece of the province cake. The emperor could be equally actively involved in the business of any province; he gave instructions, mandata, to both the governors of senatorial and imperial provinces. Cf. Emperor Trajan'd and Younger Pliny's correspondence; Pliny is the governor of Bithyania-Pontus, a senatorial province, but he's basically writing to Trajan on the smallest little things, from how to rule a court case to whether to lend money, to build a canal, etc. etc.. Although granted that Pliny seems a bit desperate for constant attention from the emperor, and he flatters Trajan and Trajan's wife shamelessly every chance he gets.