For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Worship requires a sacrifice. Prayer doesn't.
Cain and Abel each prepared sacrifices in order to worship God. The Jews offer lamb as a sacrifice. The Aztecs offer a young virgin girl. Christ offered himself.
In the Catholic Mass, the priest (acting in the person of Christ) together with the faithful (the body of Christ) offers bread and wine (Christ's body and blood substantially) to God.
Prayer is nothing but a real conversation with our Creator if you take it in a real sense. Otherwise, prayer is nothing but a ritual or a discipline.
Prayer is not a one-way traffic. Ask what you want and listen to Him patiently. (Phil.4:6). Prayer in true sense is purely a personal one. While you pray, you should be in spirit realm and at that time God comes closer to you (James. 4:8).
God answers your prayers in three ways: Yes..... Wait......No (I have something better).
Worship, which includes praise, can be done in a group. It can be done in a worshiping place. We glorify God during worship, which includes prayer, music. Collective praise and worship is powerful, during which we glorify Him in one voice.
In any case, during prayer and worship we come closer to God so that we rededictate ourselves for a deeper fellowship with him.