"Vaguely"?!  Really?!  I've explained this in great detail, ... but whatever.  Let me see if I can clearly explain how these subjects interrelate:
Various figures of differing fame have proposed teleological arguments for the existence of God (technically any god, but for all practical matters, this mostly concerns the Christian God).  These arguments from design are described in the Teleological argument article.  They are rarely referred to as simply "intelligent design," and thus, have little to no claim to that term for its common name.
A specific teleological argument is presented as science and an alternative to evolution.  This purportedly scientific theory is called Intelligent design (ID) and it is described here, in the Intelligent design article.  It is not necessarily associated with the Discovery Institute, and therefore claiming that this is the "DI version" is inaccurate.  There are no strict "versions" of the teleological argument anyway; there are different arguments from design made by different people, and they are identified by the philosopher/theologian who proposed them.
From my perspective, the articles are well-organized, though not above improvements.  If the name of the article on the "scientific theory" is a problem, we ought to have a discussion about the names of these articles, instead of trying to manipulate the lead of this one and obscure its topic.  If "Intelligent design" is deemed to be the common name of the subject currently described in Teleological argument, there needs to be a discussion with the folks there to change the name.  This article can then be renamed to something else (in the past, I've suggested adding creationism to the title).
For a less verbose explanation, see dave souza's comment above.    (talk | contribs)