After I’ve read the Texture Map Input page at blender.org, which I felt not clear enough to me, I was seeking for a more explicit document about the topic, with geometric transformation examples. I’ve found a reference to a document on the page Making Sense of Texture Mapping at blendernation.com, but the link it gives, lead to a “ 404 Page Not Found ” error. Search engine caches does not help either.
The more work I’ve done in 3D, the less I use the basic texture mapping modes. These days, I find that almost everything I do has UV coordinates (occasionally Global or Generated for the simplest of things). If I were you, I wouldn’t put a ton of time into learning the ins and outs of these different mapping modes. UV Unwrap instead. For important stuff, the main Unwrap with seams work flow is quick, fairly simple and produces great results. For less important stuff, Smart Project is one-click easy and produces fair to decent results.
What specifically are you trying to texture right now?