Box modelling is when you start with a box and then start to change the surface of the box and start to mould it too what you want. Box modelling is more used for single, rounder models such as helmets. this method is good for keeping track of the number of polygons and concentrating on one sole piece.
Extrusion modelling is when you start with a box but then extrude the faces of the box to make something that way. Extrusion modelling is used for models that have multiple extremities so that you can extrude out parts and edit them.
Autodesk Maya is 3D computer graphics software that lets you create 3D assets to use in things like video games, movies and TV. Cinema 4D is a 3D modeling, animation and rendering application. Blender is a free and open-source 3D graphics program.
All of these programs are almost the same just with different focuses and tools, Maya is more focused on making models and texturing them, which goes nicely with another program like the Unreal Development Kit (UDK). However that isn't to say that the other programs are useless, Blender is very good at rigging up a 3D model for posing and expretions and Cinema 4D has lots of tools to help with lighting and staging for animations.
All of these programs are almost the same just with different focuses and tools, Maya is more focused on making models and texturing them, which goes nicely with another program like the Unreal Development Kit (UDK). However that isn't to say that the other programs are useless, Blender is very good at rigging up a 3D model for posing and expretions and Cinema 4D has lots of tools to help with lighting and staging for animations.