What is the difference between a brother and a priest?
A priest is ordained and a brother is not. Ordained persons perform sacramental ministries such as Mass, confession, anointing of the sick, etc. whereas a brother, since he's not ordained cannot.
A brother is always "religious" meaning that he's part of a community (i.e. Dominicans, Franciscans, etc). A priest may be religious (part of a community) or secular (only under the authority of a bishop, i.e. a diocesan parish priest).