If people are to talk turkey, they are going to have an honest and open dialogue, usually with the motive to move forward through a problem. It is an American phrase that goes back to the early 1800s.
Originally it meant to talk agreeably or pleasantly, which is almost an complete reversal to its current meaning, though if the motive is to move through a problem, then all parties should be reasonable amicable. Last century, the phrase went from agreeable to honest when the phrase changed to talking cold turkey. And it then was shortened to its current form.
The compound noun cold turkey may have derived from this phrase, but it is unlikely since the meanings are so different. To quit something cold turkey is to immediately stop the action without any tapering off or help. It is usually used in reference to quitting a drug or addiction, from which there will be withdrawal symptoms.
There is no definitive answer as to the origin of the phrase. The most offered explanation is that families and friends talked agreeably with each other after Thanksgiving dinner. Another anecdote is that when pilgrims and American Indians traded, the American Indian said once, “You come to talk turkey?”