Difference between prayer and supplication
Supplication is a prayer in which you request God for fulfilling some your wish while prayer is a simple way to connect to the God without asking or requesting anything. When you do prayer you may address God by any name that makes you feel closer to him but in Supplication you simply pray hard and place your request humbly in front of God.
You do payer to thank god for whatever you have and for all the goodness in your life. You tend to credit all your happiness to his love and you extol the power of God. Supplication does not involve thanking god but it is about asking for something that you think he can give but it does not mean that it is about the selfish wishes only. People may supplicate for the well being of all, they may ask for happiness for all and for the entire mankind.
Prayer is a more personalized way to connect to God while supplication keeps God at a distance and you ask and wish things from him by placing him as the most powerful entity.