Lightfastness is a pigment or dye's resistance to change because of exposure to sunlight and atmospheric conditions - it could change hue or fade.
The permanence rating of paint includes its lightfastness but adds the additional consideration of durability of the binder. In modern times professional paint-makers will only ever use durable binders so it is highly unlikely that anyone will experience problems, and hence permanence is now less often used in this context.
When 'permanent' is used in the name of a colour as in 'Permanent Alizarin Crimson', is it referring to lightfastness, as the colour will be a modern replacement for a non-lightfast colour. The terms are often used interchangeably.