CuraEngine is a powerful, fast and robust engine for processing 3D models into 3D printing instruction for Ultimaker and other GCode based 3D printers. It is part of the larger open source project called "Cura".
MatterSlice is a C# console application that generates GCode (hardware control) for 3D printing. It was originally ported from CuraEngine (another great open source 3D printing engine). It is the primary slicing engine for MatterSlice and under constant development.