there are aspects of all these different systems in Islam, but to brand them uniquely by those names is not the practice of a purely islamic system.
Abul a'la mawdoodi gave an excellent example of the three blind men who went to the zoo to visit an elephant and find out what it's like, one grabbed the leg, one the ear, and the other the tail.
they came back and one said it was like a tree trunk, the other said, no, ur wrong, it's flat and wide like a large leaf, the other said, no, ur both wrong, it's long and thin like a rope.
simply because they had only come across certain aspects of it and not checked out the whole body.
there are aspects which are described as "capitalism", others as "socialism" (the welfare system), and some even call it materialist and worldly due to it's encouragement of satisfying natural desires (within the limits) and because it includes the state and economy into the whole), others believe it's just humble restraining from worldly desires,
to marry it with a term like socialism or capitalism is akin to narrowing it's vast encompassment of every field.
Islam - simply put - is Islam, it is totally self contained and doesn't need other brand names added to it.
it is a COMPLETE way of life (deen), and holds a just balance between the extremes and excesses of all those man made systems which fall apart every few centuries.
here's an excerpt from a book which i read a few years back which delves into detail, many of the aspects of Islam, and describes the fundamental structure well:
exerpt from :
POLITICAL THEORY OF ISLAM
By S.Abul A'la Maududi ( 1960 )
THE CORRECT APPROACH
With certain people it has become a sort of fashion to somehow identify Islam with one or the other system of life in vogue at the time. So at this time also there are people who say that Islam is a democracy, and by this they mean to imply that there is no difference between Islam and the democracy as in vogue in the West. Some others suggest that Communism is but the latest and revised version of Islam and it is in the fitness of things that, Muslims imitate the Communist experiment of Soviet Russia. Still some others whisper that Islam has the elements of dictatorship in it and we should review the cult of 'obedience to the Amir' (the leader). All these people, in their misinformed and misguided zeal to serve what that they hold to be the cause of Islam, are always at great pains to prove that Islam contains within itself the elements of all types of contemporary social and political thought and action. Most of the people who indulge in this prattle have no clear idea of the Islamic way of life. They have never made nor try to make a systematic study of the Islamic political order the place and nature of democracy, social justice and equality in it. Instead they behave like the proverbial blind men who gave altogether contradictory descriptions of an elephant because one had been able to touch only its tail, the other its leg, the third its belly and the fourth its ears only. Or perhaps they look upon Islam as an orphan whose sole hope for survival lies in winning the patronage and the sheltering care of some dominant creed. That is why some people have begun to present apologies on Islam's behalf. As a matter of fact this attitude emerges from am inferiority complex, from the belief that we as Muslims can earn no honour or respect unless we are ably to show that our religion resembles the modern creeds, and it is in agreement with most of the contemporary ideologies. These people have done a great disservice to Islam, they have reduced the political theory of Islam to a puzzle, a hotch-potch.
They have turned Islam into a juggler's bag out of which can be produced anything that holds a demand ! Such is the intellectual plight in which we are engulfed. Perhaps it is a result of this sorry state of affairs that some people have even begun to say that Islam has no political or economic system of its own and anything can fit into its scheme.
In these circumstances it has become essential that a careful study of the political theory of Islam should be made in a scientific way, with a view to grasp its real meaning, nature, purpose and significance. Such a systematic study alone can put an end to this confusion of thought, and silence those who out of ignorance proclaim that there is nothing like Islamic political theory, Islamic social order and Islamic culture: I hope it will also bring to the world groping in darkness the light that it urgently needs, although it is not yet completely conscious of such a need.
it does however seem that the original american system of "republic" has taken from many of it's aspects including a fixed body of laws and inalienable rights (constitution and bill of rights) etc. (the founders took a significant interest in Islam and seem to have incorporated much of it's methods into what was once america).
but as the Prophet (pbuh) explained by drawing lines in the sand, there are many lines which lead in different ways and only one is stable.
the american system has already fallen apart and they're now trying to call it a "democracy",
and the economic usury based system - well we can see it's fruits.
here's a video that explains the "beurocratic" aspect well.