Definition: Given two points on a circle, the minor arc is the shortest arc linking them. The major arc is the longest.

Try this Drag one of the orange dots.
Note how the points define both a major and minor arc.

Two points lying on a circle actually define two arcs. The shortest is called the 'minor arc' the longer one is called the 'major arc'.
In the figure above, if you were to refer to the 'arc AB' you could mean either one.
Typically, if you don't specify which, readers will assume you mean the minor (shortest) arc.
If there is a possibility of confusion, you should state which one you mean.

Another way to avoid confusion is to have another point on the arc and use all three to define it. For example 'arc AQB', would not
be in doubt since the point Q would lie on only on one of the two possible arcs.

When the major and minor arcs are the same length, they divide the circle into two semicircular arcs.
See Semicircle definition. Under these circumstances neither arc is considered to be the major or minor arc.