1. Minimal State
The regime advocated by libertarians, allows unrestricted laissez-faire capitalism.
Such a political system would allow huge social inequalities among people because it is not interested in final results (i.e. in how much someone possesses in the end and whether they possess anything at all!)
The only criterion of correctness of a property is, therefore, that one has obtained it without violation of any rights and liberties of others.
There are few variants of libertarian theory: the one allows unlimited initial appropriation of natural resources by private persons while the other demands their equal division to all members of community; the one defends laissez-faire capitalism and "passivity" of the state with the help of moral reasons, while the other primarily invokes concequentialist considerations and claims that minimal state ensures the greatest material well-being to the society as a whole. In it a person could legitimately posses everything that he himself produces, gets through exchange with others for his goods and services, and acquires as a gift.
This state is called "minimal": because it secures only a correct implementation of procedures through police and army but interferes in almost nothing else.

2. Meritocracy
A political system in which material success (wealth) of a person depends on his abilities and efforts. In other words, this is a society in which "career is open to the talents".
This regime differs from libertarian minimal state mainly in this that it does not allow that economic destiny of people is so highly determined by their initial social standing - since it forbids inheritance.
In the circumstances of developed social division of labor, such a result is best secured by the market because on it, in principle, everybody earns according to his capacity to satisfy needs and wishes of others. It is obvious that such a care for others' needs requires an effort to check what others want and an ability to take care of these wants.
Meritocracy's main difference from the welfare state lies in the fact that it does not care for needs of all the poor people - regardless of origin of their poverty - but only for needs of those of them who tried to improve their situation but failed in this endeavor because of unhappy circumstances.

3. Welfare State
In this regime free functioning of market is allowed at the stages of production and consumption, but the state interferes in the economic process at the stage of distribution of goods to protect those who are not able to earn enough for their living.
Mechanism which the state uses to attain this aim is (mainly progressive) taxation of those who earn and posses a lot and transfer of those collected resources to the poor.
It is usually advocated that the state should take as much as it can from the rich and stop with redistribution of wealth only at point when it endangers economic productivity.
A political system defended by contemporary liberals. Such a transfer may take a form of direct monetary help to the those who do not earn enough or could be given as in-kind provision. The latter means that the poor are given free or subsidized access to certain essential services such as: housing, medical care, education, etc. This redistribution of property may be more or less comprehensive. That is, the state can aim only at satisfaction of everyone's basic needs or it can try to secure much higher level of welfare to all its citizens.
There are several types of welfare state.

4. Communism
A social system in which the leading distributive principle is: "From each according to his ability, to each according to his needs".
To be realized communism asks either for material abundance - in which all the needed resources would be plentiful - or for very high degree of social solidarity - because the talented members of society would have to work hard but would not enjoy all the fruits of their labor since these would have to be shared with their less able associates.
So, the ambition of such a regime is to secure that everyone works as much and as hard as his talents and other abilities allow him, and that everyone gets as much goods as it is required for the satisfaction of his true needs. Since it is not very easy to expect that people are so ready to sacrifice themselves for each other, the most important representatives of this doctrine chose the first option: that communism will be established only after technology advances to the point where all the work will be done my machines which will produce (in huge amounts) everything that humans need. However, in the recent times many such thinkers have abandoned such a hope.

5. Strict Egalitarianism
A political regime in which all members of a society would get strictly equal amount of crucial material goods.
No agreement has been yet obtained concerning the fact which variant of egalitarianism is the best one.
The main problem for advocates of such a model is to determine what is exactly the good in respect of which all people should be equal. According to some of them everyone should be equally happy, according to others every person should have at his disposal equal amount of primary goods - which are things everyone needs for decent living regardless of a kind of life chosen, according too the third ones everyone should enjoy not only equal quantity of such goods but also equal power to use them, according to the fourth version all humans must have equal chance to attain happiness, and the like. In short, strict equality may be a meaningful ideal only if it is clearly specified in which respect people should be equal. But then it is necessary to propose a kind of equality that does not have unacceptable consequences. For instance, to make everyone happy would also mean to help ambitions of psychopaths who enjoy only if they torture others; to supply everyone with equal amount of primary goods would imply that handicapped people must be less happy because they have to spend more resources than others just to attain (if at all!) the level of ordinary functioning, etc.