The former has an impeccable orthodox pedigree. Lenin in his State and Revolution described the capitalist state as an instrument of the bourgeoisie, of the owners and directors of capital. Therefore regardless of the appearance a state forms, whether liberal/social democratic, authoritarian, or fascist, they share a universal inner core as guarantor of class power and capital. Following from Marx and Engels's observations about the revolutions of the 1840s, and against the revisionist positions of German SPD thinkers like Eduard Bernstein and Karl Kautsky, Lenin felt compelled to bend the stick in this direction to clearly bring out the class nature of capitalist states against those who would obscure it. This was exported into the official communist movement, and from there found itself informing the theologies of Trotskyists, Maoists, anarchists, and assorted libertarian Marxist currents. The state is a class dictatorship and the job of Marxists is to work for its overthrow and replacement by the democratic organisation of the workers.
As far as Poulantzas was concerned, this viewpoint was too simplistic and cannot account for immediately obvious phenomena. Such as why the political representatives of the various fractions of capital compete politically to keep social democratic parties, regardless of how institutionalised and integrated into the established order they are, from office. It's almost as if the right has an instinctive distrust of state power lest it be used against them, a fear that shouldn't be there if the state was a straightforward organ of capital. The second observation touches social security. In the late 1970s prior to the assault on the social wage, conservative and social democratic governments alike expanded the welfare state. Adherents of the instrumentalist view have usually explained this in terms of concessions to the labour movement, but that suggests pressure can be exerted over the state for it to act against the interests of capital. Both therefore point to the necessity of a more complex and nuanced approach to the state.
The economist approach to the state comes back to our old friend the base/superstructure metaphor from the 1859 Preface. Oft interpreted in a mechanical, strictly undialectical manner in which 'the economy' is positioned as the active element and the rest of society, its 'superstructure' (and therefore the state) as the passive recipient of its instructions and imperatives. This kind of interpretation of Marxism was a key prop cited by various Post-Marxist types in their jettisoning of historical materialism while, interestingly and contemporaneously, politicians of the centre and the right couched their market fundamentalism in terms not far removed from affirming a crude, unidirectional relationship of determination. Poulantzas however notes an alternative economist reading of the arrangement. Here, again, the economy is an active element, but one with its own terrain and specificity. Supposing it a discrete set of social relations with their own rhythms and tendencies, we're but a hop, skip, and a jump away of treating the rest of society as sets of autonomous spheres, levels, and practices.
Both kinds of economism and the expressive view are crude and wrong. Rather, there is a certain, mutually constitutive fusing between economy and state. As he puts it, "The political field of the state (as well as the sphere of ideology) has always, in different forms, been present in the constitution and reproduction of the relations of production" (p.17). This presence of the state in the economy, and the reverse, the economy's presence in the state is always conditioned by the relations of production. I.e. not just private property in the means of production, but also the state of the class struggle at any given moment. Lastly, in capitalist societies proletarians are formally separated from the labour process. They do not own the means of work, rather they are employed to give up an agreed quantity of time working for an employer in return for a wage or salary. This separation is mirrored in the relative degree of separation that exists between the state and economy (in terms of function) and in how the institutional structure of the state works (more on this in a future post).
What this means is, contrary to the expressive and economist schools, one can put forward certain theoretical propositions about the state, which is what State, Power, Socialism does. But we cannot advance a serious position about the transition from one state to another. For instance, just as Lenin's waxy corpse has been preserved for gawping tourists, so those who lay claim to his politics have been quite content to let his approach lie there without thinking about the method behind it, and so are in the habit of applying the Russian Revolution as if it's a model appropriate to every time, every place. As far as Poulantzas is concerned, the issue of transition, of socialist change, is always contingent and depends on analysing the concrete circumstances - the conjuncture. The Marxist approach to the state then is not to have a model of the state-in-general and apply it ideal-typically, but to analyse afresh in light of the experiences of our organisations and our activism. That is the Marxist approach.
More Poulantzas here.