What are some characteristics in a thanksgiving prayer? What makes it different from other prayers?
I am assuming you are referring to the idea of a prayer giving thanks rather than a prayer to be given on the American holiday Thanksgiving Day, so that's the direction I'll head. If not, I suppose the answer would be quite similar anyway.
A prayer of thanksgiving, no matter what the reason, is a message to God focused on being grateful for the the things we have in life (and really, life itself.) The focus of the prayer is to thank God for allowing us to have the chance to enjoy life, to have food and shelter and friends. It can be customizable to the specific person saying the prayer, of course.
This is in contrast to other types of prayer, which usually come in times of want, need, sorrow, or fear. In these prayers we are either asking God to provide something we need or to ease burdens we have. The contrast is roughly one of giving versus receiving.