what is the difference between focus and principal focus?

 

When rays of light are incident on a lens or a mirror, they refract/reflect to a certain point on the principal axis. This point is called the focus of the lens/mirror.

This point can be anywhere on the principal axis, depending on how the rays are initially travelling.

 

Principal focus is a special case of focus wherein the rays are travelling parallel to the lens/mirror and then refract/reflect to a particular point on the axis.

Generally the rays are parallel if the object is at infinity.