Texturing is about making a blank, lit, grey model look cool due to the artists' 2D efforts. This has nothing to do with skinning. We were all told a long time ago about skins for characters and applications that were just textures to replace the old ones, but skinning is not that. In games, skinning is about taking a static mesh (a static posed character with his arms outstretched for some reason seems to be the norm), and bending it using weighted sections that we call bones.
The vertices of that mesh are affected by sets of bones by different amounts. The weights of each bone and the bone used are stored next to the vertices so that come render time, the renderer knows which bones to use to transform the vertex, and how much of each bone transformed vert to add into the final output vertex value.
If you only use one bone per vertex, and always have a weight of 100% for that bone, then you end up doing stitching, this is where sections of the mesh are moved solidly, and some polygons stretch to cover the gaps at the joints. This method worked well on the ps1, and is used for some ps2 titles, and using blended joint sections, this method is good for the Wii also.
So, Skinning is about bending a mesh to make it look like it's a soft animated body, stitching is about using solid sections with some polys stretching to cover the gaps, and textureing is about usig the 2D stuff. Hopefully we won't have to go over this again :)