What does it mean in each of my contact lenses have different axis?

Question

prescription is

left eye is +20.00

right eye is +120.00

Answer 1

There is an astigmatism correction.  Such lenses have a small dot to facilitate installation at the correct angle.  The complete specification for a lens consists of a spherical correction, which is just a number without an associated direction, and a cylindrical correction, which involves two numbers: the strength of the correction, and the angle at which it is applied.

Answer 2

This is just a misunderstanding.

The right eye is always first.  Always.

Axes are always expresses in degrees; never in any other way.  The axis will always be a number between 1 degree and 180 degrees.

It is not unusual for the axes to be different.