If ID originated as creationism with the explicit references to God and the bible removed in order to circumvent US laws regarding the teaching of religion in schools, then
- ID is a form of creationism,
- its claims are a subset of those of creationism, and
- the lack of references to the Genesis account does not invalidate these.
That many leading IDers are very coy about what they believe actually happened is consistent with the above. That you conveniently forget this possibility is also consistent with the above, as is your failure to ever produce any evidence against it.
All creationists in the sense specified accept that the world is designed, but not all those who accept that the world is designed are creationists in the sense specified. Creationists are a subset of those who believe in design, not the other way around.
Creationists are a subset of those who believe in design because ID is a subset of creationism.
Just as Vegans are a subset of vegetarians because vegetarianism is a subset of Veganism.[1]
You should learn set theory. It may increase your understanding.
Veganism: Do not eat meat. Do not eat dairy products. Do not eat eggs.
Vegetarianism: Do not eat meat. ↩︎