If you ate in conflict with yourself you can not be at peace with yourself. If to countries are in conflict they can not be at peace. Even if a war never happens, peace can't happen because the conflict is always present. People or countries can disagree with each other and not be in conflict if they don't try to change the other to conform to their viewpoint. You can disagree and be at peace, but you can't be in conflict and be at peace
Between countries, peace is defined as the absence of conflict. There may be an agreement or treaty between two countries that both are abiding by, or they may just be co-existing without paying attention to each other, but as long as there is no tension, no hostility, no conflict the situation can be called peace, or peacetime.
An absence of conflict isn't peace. True peace is when someone is happy and content in his or her life. Someone can have an absence of conflict but still be unhappy or upset, both of which is hardly peaceful. Countries are the same way--two sides not at war doesn't mean there is no conflict. There can be internal struggles between political forces in one country that belies any peaceful intentions. (Example: Dems versus GOP in Congress right now.)