I saw this kind of explanation in several textbooks but I’ve never understood it completely. Both examples seem to be the same, and still we use both definite and indefinite article.
Yes, it’s a difficult point to grasp and has a lot to do with how you are thinking of the object and how it seems to you.
As you say, both seem to point in the same direction. I could say: The horse is a noble animal. I could also say A horse is a noble animal.
I could say: A book is a treasure of knowledge. I could also say: The book is a treasure of knowledge.
In both examples using ‘the’ I am not thinking of the horse I know or have mentioned before or the book I have read and have mentioned before. What I am doing is putting the objects: horse book on a pedestal. I am in a way revering them both and showing great respect to both by using the definite article the and not the indefinite article a