Off the cuff and generally speaking, we can say a ‘Deep State’ is a state that harbors a potent mini stealth state within its formal self. ‘State capture’, particularly if it is effected by a more structured entity of a given social formation, (say a class, like a reigning plutocracy) is much more general and comprehensive. Nevertheless, we have been using, rather lazily, the phrase ‘captured state’ as a short hand or as a substitute for a ‘deep state.’ Strictly speaking though, ‘deep states’ arise in complexly organized societies. May be it is better to confine its use only to those countries that are at the core of the world system and to exceptional ones in the semi-peripheries. 
A deep state manifests a structurally, institutionally and to some extent culturally entrenched stealthy operating power within the formal ambit of a constitutional order. The thuggish capture of states, i.e., vandalized estate-ization of weak states, as is the case in many of the ‘banana republics’ don’t belong to the category of deep states. Initially, the idea of a deep state gained currency in the attempt to explain ‘the state of the states’ in countries like Turkey. Our not-so-learned conviction is; deep state is a phenomenon that obtains, almost exclusively, in the advanced industrial countries of the west! Naturally, global establishment will not favor such a characterization of the leading/core countries of the system. Certainly one can hardly reflect/learn such subversive sounding concepts in the Ivy Leagues. This is one of the reasons why we the unlearned in our characteristic vulgarism call their pompous associates ‘Ivy idiots’!
Here is another version of a deep state, which we don’t fully subscribe to. The phrase as it was coined in the particular case of Turkey goes something like this. A “Deep State” is a system composed of high-level elements within the intelligence services, military, security, judiciary and organized crime.’ To us this sounds more like an outright criminal, though temporal, capture of a state (a la Mobutu’s Zaire.) Mike Lofgren’s definition is more to our liking. It is ‘… a hybrid association of elements of government and parts of top-level finance and industry that is effectively able to govern the United States without reference to the consent of the governed as expressed through the formal political process.’ Mr. Lofgren has written a lucid and we might add, excellent expose about the ‘deep state par excellence!’ As an American who has spent almost three decades as a congressional aide, we think he knows what he is talking about.
Since the Lofgren’s expose has relieved us from the task of meddling through the concept of a deep state, we will devote the remaining space/ink to deliberate on clear and present dangers, mostly associated with captured states. The former definition, which is a rather inadequate characterization of a deep state, ‘… high-level elements within the intelligence services, military, security, judiciary and organized crime’ actually is more relevant to our (third world) predicament, i.e., the thuggish capture of states. In the particular case of Egypt for example, we can say the country is probably closer to a deep state than any of the other African nations. In fact it is because of this subterranean powerful state within the formal state (not much power here) Egypt is having a problem coming up with even a semblance of formal, content-less democracy!
On the other hand, in the not-so-deep or shallow states (many of our countries on the continent) the beast can actually name the individual culprits (in person) that are creating havoc in the affair of the states. These psychopaths, by undermining democratic tendencies and the proper functioning of the bureaucracy, end up alienating the beasts (human mass) from the states, however pro-people as well as developmentalists the concerned states are or might be. What absolves our case (weak and shallow states) is; there is no systemically entrenched malice underlying our states. We reiterate; the idea of a ‘deep state’ is a manifestation of strong states with democratic facades. For example China is a strong state that is also a dictatorship; a dictatorship of the people via the communist party, not a dictatorship of capital via the plutocracy (at least so far.)  In this regard countries like Russia (BRI_S, etc.) have yet to make up their minds. Perpetually aggressive (wars), irresponsible (climate change, etc.) & callous (pauperization of labor) accumulation is the typical feature of deep states, facilitated by psychopaths-dominated subterranean state. The thugs/goons, of shallow states, be them members of the ‘… high level element of the intelligence services, military, security, judiciary and organized crime’, including the oligarchs are all identifiable and can be dealt with, if there is a political will to do so, (by the kosher power that be) unlike those legal criminals (not an oxymoron) of deep states (banksters, etc.). Remember our definition of an oligarch? To us sophists, an oligarch is someone who steals his/her way from rags to riches!
When current revolutions are obliterating all kinds of states left and right by waging wars, not in the thickest of bushes, but rather in the glittering squares of metropolises, we believe the likes of our governments are taking unwarranted risk by delaying the delivery of comprehensive justice (economic, social, etc.) to their abused beasts, (mostly caused by connected psychopathic goons.) About two decades ago Bosnia’s streets were bloodbaths, because of so-called ethnic problems, today these streets are fomenting collaborative revolution against an economic system run by psychopathic parasites. When people demand justice, justice must be delivered by hook or a crook! Otherwise and sooner than later, the beast will force justice, equity, clean government, etc., in one form or another. Therefore delay, besides undermining credence, might well create dangerous instabilities (Ukraine, Venezuela…) Frantic attempts to salvage situations once the beast unbolts, might end up being just another case of: “Too little too late.” Good Day!