What are the two coordinate systems on locating places?

Rectangular : two distances (preferably at right angles)

and polar : a distance and a direction.

There are two systems currently in use.

One is referred to as Geographic Information System (GIS), which is a very complex system which you might envision as cutting say a 2 inch square section out of a basket ball or soccer ball, then flattening this piece out. A flattened out portion of the Earth is then flattened and represented on a map. You can imagine how the edges of the ball get distorted as they want to stay curved (actually spherical).

The second coordinate system is the more commonly used Latitude and Longitude. The numbers you see represented when using your GPS (Global Position System).