So there are two pieces to what someone might call a Coordinate System
The first is a Geographic Coordinate System or GCS, which is what WGS84 falls under. The definition given by ESRI states that a GCS uses a three-dimensional spherical surface to define locations on the earth. Basically, a GCS is used to define your real world points on a 3 dimensional digital surface. Examples of this include WGS84 (World Geodetic Survey 1984), NAD83 (North American Datum 1983), or NAD27 (used before NAD83. North American Datum 1927)
The other is a Projected Coordinate System or PCS. A PCS is used to take those points that you defined with your GCS and translate them to a 2-dimensional surface. This is what people commonly refer to as a "projection". This can include things like Robinson, Albers Equal Area, and (one of my personal favorites) Waterman butterfly.
These are different parts and are made up of different pieces, but both of these together create a coordinate system. This is the very simple definition of both, but if you want to get into the math of everything, ESRI has good documentation in their resources section discussing map projections. Wikipedia's page on map projections also does a very good job of explaining the different types of PCSs, what distortions are caused, etc. Many projections also have their own pages explaining their history, math, etc.