How would your definitions cope with a non fire rated door that had been upgraded either by one of the historic techniques such as were common in the days of BS459 or by one of the proprietory methods such as intumescent varnishes and paints? Would you then need a further category - upgraded door?
Personally I think you are opening a whole can of worms here and I cannot yet understand what is behind our proposal. I accept I may be being thick as usual Eli but I cannot see why, for whom and for what benefit. Is this for risk assessment or fire audit purposes?
My opinion is that there are too many box tickers and further checklists and labels will not help. What is needed is an educated assessment of each door and its frame, its condition, construction, history, data available, and door furniture within the context in which it is placed.