Movielens, I believe, employs item-by-item collaborative fittering.

Correct me if I'm wrong but I think movielens uses item-item collaborative fitering. Wizard and Warrior might be pure collaborative filtering vs a mixture with content based filtering (such as additionally using year, genre and tag information).

I'd really like to know what's hiding behind the two algorithms, even in simple terms.

This is an interesting proposition. I am puzzled about how this request could be met. I see currently there are four recommenders: "the peasant," "the bard," "the warrior," and "the wizard." I would like to see better descriptions of those recommenders, e.g., what makes "the warrior" different to "the wizard" since both are based on ratings. For that reason I prefer to know how these recommenders see a movie, that is, I imagine movies are more that an id tag but also have qualitative or quantitative aspects such as genre, director, actors, tags, etc., which may or may not play a part in how predictions are made. I understand some AI could make its decisions based on abstract structures that are not as easy to follow as decision trees. Thus, I imagine in some cases it may not be a trivial matter to describe how a recommendation or prediction comes out.

Yes, much like pandora does for songs. I'd like to see this feature very much!