Many years ago there wasn't Halfords Advanced, it was only Professional. I believe the tools were made for them by Snap-On, but that could just be hearsay or whatever. That arrangement went and they released the Advanced range, of which some of the tools are called Advanced Professional for reasons I can't quite discern.
Advanced or Professional, the tools are still very decent quality for the money. They have a fairly wide range of useful tools available at short notice in store as well which does come in handy, although they used to carry absolutely everything in bigger stores and now a large chunk is online only.