Can somebody please explain what is the difference between the Coordinate system (WGS 84 for example) and a Projection (Universal Transverse Mercator for example)?
What is the difference between a projected coordinate system and projected CRS
Both examples are coordinate systems. The difference is that WGS 1984 is a geographic coordinate system, and UTM is a projected coordinate system. Geographic coordinate systems are based on a spheroid and utilize angular units (degrees). Projected coordinate systems are based on a plane (the spheroid projected onto a 2D surface) and utilize linear units (feet, meters, etc.).
To answer your second question, a coordinate system (whether geographic or projected) and a coordinate reference system refer to the same thing.