The peace of Christ is truly different that any "peacefulness" we can feel. It is not of human origin. It's truly divine.
During the past year, I have been blessed to experience this peace.
In the past, I always thought that the peace of Christ was a general serenity I would experience in the absence of stress. For example, when I practiced a stress-reduction exercise--which could be as simple as deep breathing--I could feel my muscles relax, my heart beat slow, and the general stress begin to leave my body. The stress from within was then moved without.
I was certainly wrong in expecting the Peace of Christ to be of this human nature. This is but one way I can describe it.
When the Peace of Christ enters, it comes from without and moves within. It feels to me like a stream that enters me then begins to puddle and fill my soul. This Peace is not the absence or removal of something--such as stress--but the infusion of Christ, by the power of the Holy Spirit.
It is easy to recognize, as it is nothing that we humans could possibly conjure up or force to happen. It is not an emptying but a filling, and it is complete.