When you place a cone on the Earth and unwrap it, this results in a conic projection. Examples are Albers Equal Area Conic and the Lambert Conformal Conic.

The azimuthal projection plots the surface of Earth using a flat plane. For example, common azimuthal projections are gnomonic, stereographic & orthographic

Universal Transverse Mercator (UTM) segments the Earth into 60 zones (each UTM zone is 6°) and projects each zone with an upright cylinder of its own.

When you place a cylinder around a globe and unravel it, you get the cylindrical projection like the Mercator, Transverse Mercator and Miller projections.

Ellipsoids, survey benchmarks and triangulation – these are the ingredients for geodetic datums. NAD27, NAD83 and WGS84 are common datums in North America.

The best way to represent the Earth is with a globe. But map projections can be awfully useful too. Find out why cartographers use map projections in GIS.

For ArcGIS projections, define projection changes the metadata describing the current projection. The project tool changes the projected coordinate system.