SEPERATION OF POWERS BETWEEN THE INSTITUTIONS
Separation of Powers  is a representation of the government of a country where the different parts of the government are assigned with different purposes. It refers to the institutions of the government. In the United States of America, these different purposes are judicial, legislative, and executive. Checks and balances  is a means through which the government makes sure none of the aforementioned areas can operate on their and that they need one another. It is the method of governance. This is designed so that one single entity cannot take majority control.
This can be thought of different institutions who are sharing powers amongst themselves. Each of the institution of the government (executive, legislative, and judicial) does not have to depend upon each other as far as its power is concerned. For example The Congress cannot be named or dismissed by any member of any political party (such as the President). Each of them has powers of their own. Nonetheless, to perform certain tasks of the government and to get anything done altogether they have to rely on each other. This harmony has to be maintained in order to keep the whole body of the government working. The Congress can pass laws, but they cannot execute them. The laws must be put into operation by the president dependably, those which are passed by the Congress. But the President is limited by the amount of money which is passed by the Congress. 
The Separation of Powers and Checks and Balances kind of have common characteristics, but the doctrine of the latter refers to the ability of one branch to restrain the activities of another. For example: the power to make laws lies within the legislative branch, but the power to cancel or limit them lies within the ability of the judicial branch, assuming that the law was unconstitutional.
The 'Separation of Powers' doctrine basically explains that the powers which the different branches of the government possess constrain their ability to carry out a law accordingly. For example the judicial branch can't pass laws because that power is reserved for the legislative branch. This concept gets more complicated when the concept of ‘common law’ comes into play. Similarly, foreign policy cannot be dealt with by the legislative branch. They cannot implement laws because that power is reserved for the executive branch. One more example of the Separation of Powers doctrine is the 'political question' doctrine that the judicial branch sometimes applies when they are making decision on cases. Under that doctrine the courts will not imperative on a case of they think that the decision will come to cross paths with a power that is reserved for another branch. 
In real life this all gets much more complicated as in practice the powers of the different branches do overlap with each other. In real life it can be seen that certain thing are controlled by certain branches even though in theory it should in control of the other. Such an example may be that the federal courts are somewhat controlled by the legislative branch which in theory one may think falls under the jurisdiction of the judicial branch.
AN IN-DEPTH ANALYSIS OF THE THREE BRANCHES OF THE GOVERNMENT
Our Constitution is a result to the actions that took place preceding it. The constitution’s founding members had many goals, the most important of them being the measure to avoid tyranny. For doing so quite a few diverse systems were set up so that the misuse of power can be prevented. One of such systems was Federalism  . In order to equilibrium the power of the national and State governments Federalism was formed. This procedure limited the power of the government. 
Checks and balances is another system that was developed beside the separation of powers. Checks and balances, or the separation of powers, is based upon the philosophy of Baron de Montesquieau. In this system the government was to be divided into three branches of government, each branch having particular powers.
In this branch laws are made
In this branch laws are enforced and carried out
In this branch laws are interpreted
Each branch of the government has power within them and as well as they have powers over the other branches of the government. This is designed so that one single entity cannot take majority control and to prevent one to portray monopolistic activities. For example:
Congress may pass laws, but the President can prohibit them.
The President can reject laws, but Congress can overrule the rejection with a 2/3 vote.
The President and Congress may agree on a law, but the Supreme Court can declare a law illegal.
The President can assign Judges and other government officials, but Senate must grant them.
Supreme Court judges have life terms, but they can be put on trial.
SEPERATION OF POWERS FACILITATES AND ENSURES CHECKS AND BALANCES
In a democratic country the constitution determines how the political power will be distributed. It is the harmony of the effectiveness between the constitutional provisions, the political predispositions and capabilities of those managing the executive, legislative and judicial branches that determines how fluidly a government of a country operates. There are periodic votes taking place to elect the political leaders. As long as they are in the government, they are expected to follow the legislature. Checks and balances to the policies, performance and activities are applied to the key governance institutions by the legislators to ensure that they obey the rules to the provisions of the constitution and the rule of law and due process of law, and that they deliver their electoral authorization. The individuals involved in the formation of the government will be held responsible for every action they perform and hence they should be careful while implementing the policies. The media makes sure that the government and its civil servants carry out its due duties and that they are held responsible for their actions. Transparency from the government is also demanded so the general population has idea about what is going on within. 
Each of the institution of the government (executive, legislative, and judicial) does not have to depend upon each other as far as its power is concerned. They each have separate and independent powers. Nonetheless, to perform certain tasks of the government and to get anything done altogether they have to rely on each other. This harmony has to be maintained in order to keep the whole body of the government working. The Congress can pass laws, but they cannot execute them. The president must implement the laws authentically, those which are passed by the Congress. But the President is limited by the amount of money which is passed by the Congress  . 
The separation of power is greatly needs but its effect is weaker than ever. More and more new institutions are being formed to try and ensure a better environment for checks and balances and general oversight of the executive. Example of such an institution is the ombudsman and the human rights commission. 
THE LIMITATION OF THE SEPARATION OF POWERS WITH A FULLY DEVELOPED SYSTEM OF CHECKS AND BALANCES
The limitation of the model was that it is based upon the values held by the founding members of the country. These values were not based upon principles according to which a country should be run, but from an intellectual and emotional attachment of the classlessness according to which the country was run. In the beginning the American government banned monarchy and aristocracy, only keeping republicanism. It could not be specifically claimed that checks and balance were the national accessories of separated powers without sacrificing the very core of republicanism. What could possibly represent the people in the legislation if it were not the people in the first place? It is actually a logical matter that as opposing to the republican theory the separation of power compelled the Americans to discard the superiority of the legislature. The federalists were wary of the danger of dangerous usurpation by the few, the unavoidable and the current pressure of the “artful and ever active aristocracy". The founding members can be criticized for not only carelessly wanting to arrange a native aristocracy, that is the Senate, and a monarchy, that is the presidency, but also forcing them to enter in a mixed government who can remove major threats to privilege. 
The separation of power is the common factor which defines the characteristics of the relationship between the congress and the presidency and their contribution to policy. It not only defines the principle according to which a government must operate, but it also make sure that the power is not abused by any one of the branches of the government by safely dividing it. By dividing the power unambiguously to different branches of the government, the designers of the constitution made sure that the internal competition of the various institutions of the government maintain the self-preserving power and hence the process their individual liberties. The separation of powers established the institutional structures and the operational rules of the political game, while at the same producing an active vagueness within government that ensures jurisdictional tensions and differentiation disagreements at the highest level of government. It is through the separation of powers and its respective checks and balances that the presidency and the congress face each other and also learn to coexist with each other. The separation of powers offers a fundamental framework of constitutional orientation which does not only inform dispute. It motivates political appointment and penetrates calculations of every office-holder in a country.