Definitions

Aid-in-dying:

Aid-in-dying has multiple meanings: withdrawing or withholding life-sustaining treatment, physician-assisted suicide and/or euthanasia. See: The Model Aid-in-Dying Act, § 1-102(3) ("'Aid-in-dying' means the withdrawal or withholding or other abatement of life-sustaining treatment or the administration of a qualified drug for the purpose of inducing death").
Conflations & ConJobs: 

Conflation & ConJobs is a moniker used by the disability rights group, Not Dead Yet, for the assisted suicide/euthanasia group, Compassion & Choices.  Compassion & Choices was formerly known as the Hemlock Society. 

Doublespeak:

Doublespeak means "saying one thing and meaning another, usually its opposite." An example would be the definition of "self-administer" in Washington state's assisted suicide/euthanasia act, which allows another person to administer a lethal dose to the patient. See e.g. Margaret Dore, "'Death with Dignity': What Do We Advise Our Clients?," Bar Bulletin, King County Bar Association, May 2009 (scroll down to the paragraph headed "Self-administer" ).  Another example would be the prohibition against euthanasia in the Washington act, which is defined away in the next sentence.  See here:  Scroll down to paragraph headed "Counter Arguments."

Euthanasia:
The American Medical Association (AMA) states:  "Euthanasia is the administration of a lethal agent by another person to a patient . . ."   (AMA Code of Medical Ethics, Opinion 2.21).

Mercy Killing:

Mercy killing means euthanasia. See http://education.yahoo.com/reference/dictionary/entry/mercy%20killing

Physician-assisted suicide

The American Medical Association (AMA) states: "Physician-assisted suicide occurs when a physician facilitates a patient’s death by providing the necessary means and/or information to enable the patient to perform the life-ending act." (AMA Code of Medical Ethics, Opinion 2.211). For example, a "physician provides sleeping pills and information about the lethal dose, while aware that the patient may commit suicide." Id.

Terminally Ill 

"Terminal" does not necessarily mean dying. The Washington and Oregon death with dignity acts apply to people with a "terminal disease," which is defined in terms of a prediction of less than six months to live. These predictions can be wrong.  See e.g., Nina Shapiro, “Terminal Uncertainty: Washington’s new 'Death with Dignity' law allows doctors to help people commit suicide - once they’ve determined that the patient has only six months to live. But what if they’re wrong?," The Seattle Weekly, January 14, 2009.

In other states, suicide/euthanasia advocates have proposed expanded definitions of terminal, which, if enacted, would apply to people who are clearly not dying. (a healthy person in a wheelchair, a 20 year old dependent on insulin and/or a young man with stable HIV/AIDS with "decades" to live).   See here and here.  "Terminal" does not mean dying.