What is the difference between a radius and an apothem?

An apothem of a regular polygon will always be a radius of the inscribed circle. It is also the minimum distance between any side of the polygon and its center.
good luck and hope that helps 

The radius is something you only find in circles or spheres .When you start at the center point and go to a point on the surface,the line segment you made is always the same length, the radius.

The apothem is used in polygons. This is because when you draw a line segment between the center of a polygon and a point on the edge, it can take on different lengths. the apothem though is always the one thats perpendicular to a side.