A PA is as it says a Personal Assistant so is normally attached to one person, normally a manager/director/boss. A secretary is normally accessed by more than one person and will normally carry out administration duties such as typing and making appointments, taking calls for a number of people.
A PA will be the life line of their boss, they will handle the post, diary, meetings, appointments etc for one person and could be said to be covering their back!
I cant think of any specific training for PAing. I think I would be looking for a calm and uber organised individual with all the patience in the world!!!
Good Luck!