What is the difference between a free market and a perfectly competitive market? I am trying to find the distinction between a free market and a perfectly competitive market, and I can't find the right definition on what makes them different. Can someone give me a clearly expressed definition on what makes one different from the other.

Please Note: I am looking for a reference based answer.
Perfectly competitive market: Numerous participants, so that no single participant has any influence.


  A perfectly competitive economic model is meant to describe a situation in which there are many participants, and the influence of each one individually is negligible. The state of the economy is thus insensitive to the actions
  of any single agent; only the aggregate behaviour matters. (Source.)


Free market: Voluntary exchanges; no coercion (in particular, no government coercion).


  "Free market” is a summary term for an array of exchanges that take place in society. Each exchange is undertaken as a voluntary agreement between two people or between groups of people represented by agents. (Source.)


Notes:


The two terms are not mutually exclusive.
Neither exists in the real world, though we can imagine examples of both.