Without going through all the duties etc. the complexity of a lifting operation depends on the hazards associated with the load path, the load itself and the equipment lifting it, and the environment in which the lifting operation is being carried out. 

The duties of an appointed person for crane operations can vary according to the complexity of the operation. The duties for a basic lift are considerably fewer and less demanding than for a complex lift. An appointed person employed for a basic lift might not be competent to carry out a more complicated operation, and another appointment could be required for this.

Basic Lift

The appointed person may make an assessment on the basis of information with which they have been provided, visit the site personally or delegate a competent person to undertake the visit on their behalf.

Intermediate Lift

The appointed person may visit the site personally or delegate a competent person to undertake the visit on their behalf.

Complex Lift

Being present on the site during a complex lift.

I hope this helps.

Added to this post, note, if the lift changes from the original lifting plan, (it happens) then the A.P. needs to adapt or change the lifting plan.  That's why the A.P. get more money than the Lift Supervisor - or so I've been informed (I am a CPCS Slinger Banksman).