I have to agree with everyone who has responded so far. I also believe that both A and B are forms of introspection, just a different way of going about it.
As for importance within a story, I believe that it is essential to a written story. Introspection gives insight into what a character thinks, feels, and believes about what is going on around them and within themselves. In the written form, lacking such insight to a character leaves a dry manuscript that reads like a screenplay. A screenplay is something that should be seen and not read, complete with visual and auditory imagery, which is the prime advantage the TV/movie medium has over the written work. Meanwhile introspection is a key tool for the written work.
On the other hand, it IS possible to overdo introspection. GASP! Yes, I know I've probably gotten myself in deep trouble here <bg>, but there is such a thing as too much.
There are examples of too much, for example, in the works of Anne Rice and Barbara Hambly, just to name two authors who stand out in my mind. The characters introspect so much that I lose track of what's been happening in their stories and need to go back dozens of pages to find out. Seventeen pages of the view from Louis' veranda in New Orleans and what he thinks of it in Interview with the Vampire is just TOO much.
While television has visual advantages, the written author's prime advantages are description and introspection, which allow understanding of a story and its characters you sometimes cannot even come close to in other media.
