What is the difference between chord length and arc length?

A chord is a straight line joining two points. (Usually of a circle, but I suppose that use can be and has been generalized.)

Chord length is, therefore, the straight line distance between two points on the curve.

An arc is a segment of a curve between two points. (Initially a segment of a circle, but generalized to a particular segment along some given curve.) The arc length is the length such a segment (Initially the length of an arc of a circle, but generalized to the length along some given path.)

In the graph below, the solid red part is an arc. The solid blue part is a chord.