Terminology: Brainwashing, Mind Control, or Undue Influence?
The term 'brainwashing' was originally coined by journalist Edward Hunter in 1950, to describe techniques used by the Chinese Communists to subvert the loyalty of American prisoners captured in Korea. Brainwashing in this original sense involved physical coercion: imprisonment, food and sleep deprivation, and sometimes torture. However, the effect of the brainwashing did not last very long after the subjects were released from captivity.
Cults use more subtle techniques which do not depend on physical coercion, and the effects of cult involvement can last for some time after a person leaves a cult. Therefore, to distinguish the more subtle techniques used by cults, from the old brainwashing model, which depends on physical coercion, some researchers writing about cults have in recent years tended to use the term 'mind control', or sometimes 'thought reform', in preference to 'brainwashing'. At the same time, just to complicate the picture, the term brainwashing continues to be used in a more informal or colloquial sense by journalists and the general public, but its meaning seems to have broadened somewhat, to include any methods used to influence a person's opinions or outlook.
Unfortunately, the term 'mind control' also has a number of disadvantages. Firstly, the term is also used outside the context of a discussion on cults, in films like 'The Manchurian Candidate', and by conspiracy theorists who claim that government agencies such as the CIA or the Chinese Communists have developed secret 'mind control' techniques (like the so-called MK Ultra programme) for controlling their citizens, or for turning people into robots.
While there is little doubt that various governments have researched the military potential in developing techniques which might be able to control people's minds, there is scant evidence that they have had any success. (Though it could be argued that some terrorist groups have successfully used brainwashing or mind control techniques to persuade people to become suicide bombers, which is not so different from the 'killer robot' idea found in 'The Manchurian Candidate' and other science fiction works.)
A second disadvantage of using the term 'mind control', even when it is clear that the term is being used to refer to a cult persuasion process, rather than as part of some conspiracy theory, is that the term is still rather misleading and prone to being misunderstood. It tends to suggest the idea of absolute control, or that a person's will can be directly overcome using some kind of advanced technology.
Which is not at all how cult mind control works. Cult mind control does not directly overcome a person's free will, but rather it influences their belief system and worldview, which in turn influences how a person exercises their free will, and the choices they make. In simple terms, a cult promotes its cultish belief system, and then believers control their own minds, as they attempt to discipline their minds and reform their personalities, in accordance with the tenets of their cultish new belief system. 
'Mind control' does not mean absolute control of a person's mind. It is a shorthand term for a complex process of mental and psychological manipulation, which occurs within a cult. It is a way of changing a person's thinking processes, through using a number of techniques, which include deception, the manipulation of trust, the use of psychological double binds, and other related techniques. 
Unfortunately, some academic researchers, sometimes collectively referred to as 'cult apologists' persist in mis-interpreting the term 'mind control' to mean some kind of absolute or irresistible control, along the robot model. For example, Dr Eileen Barker, a sociologist of religion at the London School of Economics, wrote: 'If people are the victims of mind control, they are rendered incapable of themselves making the decision as to whether or not to join a movement - the decision is made for them.' [Dr Barker's italics] 
Dr Barker also adduces as evidence that mind control (in the robotic sense) is a myth, the fact that not everyone attending a residential workshop given by the Moonies went on to become a full member.  If mind control was real, Dr Barker argues, everyone, including presumably herself, would have been irresistibly recruited .
The fact that Dr Barker is arguing against an absurd caricature of the cult mind control model might be comical if it were not so tragic. There is little doubt that Dr Barker and other so-called cult apologists have played into the hands of cults, by misusing their academic status to help discredit the claims of brainwashing or mind control by many ex-cult members.
In order to try and forestall the above sort of misinterpretation of the term mind control, some anti-cult activists and others concerned about the harm done by cults, have started to prefer the term 'undue influence'. Undue influence has been defined in English law as 'the unconscientious use by one person of power possessed by him over another in order to induce the other to enter into a contract'. 
If the parties to a transaction had a confidential relationship to one another at the time of negotiations leading to a contract, then the existence of undue influence will be presumed, and the burden of proof is on the party having the influence to disprove that it was used in an improper manner. A confidential relationship is a relationship of trust, such as that between doctor and patient, teacher and student or vicar and church member.
This legal definition limits the concept of undue influence to cases where there is a specific legal contract, involving the transfer of money or property from one party to another. But, if it is legally accepted that a person can have sufficient 'undue influence' or 'power' over another to persuade them into a disadvantageous contract, it does not seem an unreasonable extension to say that, in certain circumstances, this same 'undue influence' could extend over other areas of a person's life, to the extent that, in some cases, they leave their family and job and end up working full-time for the cult, effectively becoming servants of the cult.
'Undue influence' is probably the least misleading of the various terms which have been used to denote the manipulative techniques used by cults. The problem remains that these techniques are quite clever and subtle, and very difficult to explain satisfactorily to anyone who has not themselves experienced being in a cult. Consequently, critical ex-cult members are often not taken seriously when they try to communicate their concerns. Many ex-members experience prejudice and misunderstanding when they try to explain to the wider world how cults work and the dangers they pose. Which in turn makes it easier for cults to thrive.
See 'The Brainwashing
v Free will argument'