It is easy enough to see how "peace" got replaced with "rest" in literature and references. In chapter 57 peace is equated with rest. The troubled sea cannot rest, and the wicked have no peace.
Sometimes we read this to mean peace of mind. The wicked have no peace or rest because they are tormented with the evil in their thoughts and intentions. This torment suggests that at least they have a conscience. Their greed or lust or lack of control still leads them to evil. There are multiple causes of evil in the mind of humans, and all of them prevent peace and rest.
Peace can have several meanings: Political peace among nations, peace of heart and soul, peace within a family, peace to grow and learn. Rest, too, can mean a time to refresh and restore the body, rest from labor, and after harvest the land is at rest. In the Jewish calendar the land rested and no crops were planted in certain years. 1 Kings 4:25 speaks of the time when "every man lived in safety under his own vine and his own fig tree;" the picture of peace and rest is easy to imagine. It does not mean there is no labor, but the work is fruitful and provides grapes and figs and shade in the heat of the day.
Peace and rest are valuable, priceless maybe. They come to those with a clear conscience who have placed their trust in God. If you find yourself tormented and unable to achieve peace or rest, maybe you first should seek forgiveness. Then count your blessings. What has God done for you? Even if you have an illness or financial problems, peace can still be in your heart. As you live obediently, you will find his peace spreading in all the areas of your life.