When I recently co-authored a booklet on mating combinations, I included what I called a 'Mating Alphabet' with 29 frequently occuring mating themes (the Norwegian alphabet has 29 letters). One of my advisors asked me whether I had considered a more theoretical approach, taking the basic properties of each mate more into consideration. My answer was that, yes I did, and quickly decided that a more pragmatic approach probably would be more useful for our targeted audience. Let me illustrate my reasoning with a set of positions:
I suppose that from a theoretical point of view, they are all three more or less identical. In practical play, however, I will claim that each of them has independent value, as they all occur in quite different kinds of positions.
This, of course, doesn't imply that I find categorizing checkmating patterns an idle pastime without any practical value. On the contrary I find it a very interesting angle for further study and probably quite educating for an advanced student. As a matter of fact this may be a subject to which I will return in the near future.