When a ring is bezel set, the metal setting holding the gemstones in place lies close to the stone, creating a line of metal around the edge of the stone. Trilogy rings are any rings that prominently feature three gemstones. Sometimes the gemstones are a uniform size, and sometimes one stone - usually the central stone - is larger than the others.
Eternity rings feature diamonds all around the band. The channel setting means that the gemstones are set on the top and the bottom, with the setting sitting on level with the stones, creating a little 'channel' that the stones sit in.