"Creationism" is a broad category that includes a number of sub-categories. For example, there is young-earth creationism, old-earth creationism, day-age creationism, progressive creationism, Hindu creationism, progressive creationism and many others. Intelligent design is one of those sub-categories, which is why I usually refer to it as "intelligent design creationism".
If you look into the history of intelligent design creationism (IDC), you find that it was specifically crafted as a religious/political strategy to get creationist teachings into public schools, following a series of federal court rulings banning the teaching of Biblical creationism. After the courts' rulings, creationist organizations tried to strip their material of all overt Biblical and Christian references and themes, and relabel them as "intelligent design". So rather that creation by God, you had "design" by some unspecified "intelligence". They also dropped claims about the age of the earth, advocacy of Noah's Flood, and advocacy of special creation of human beings.
The problem was, they didn't do a very good job of covering their tracks. When the inclusion of IDC in public schools was put on trial in Dover, PA, it was very, very easy for the pro-science side to convincingly demonstrate that IDC was merely Christian creationism in a new dress. The most infamous example was when the creationists did a find and replace for the words "creationists" (find) and "design proponents" (replace) in their textbook "Of Pandas and People". It didn't quite work as well as it should, and
they ended up with "cdesign proponentists". IOW, they kept all the same arguments and material from creationism, and slapped a new label on it. So it was pretty easy for the judge to rule that IDC is merely a deliberate rebranding of Christian creationism.
Since that Dover ruling IDC is essentially dead. Because it was a political/religious strategy, it never really generated its own science, and after the court ruling no one is really trying to mandate its inclusion into public schools. Creationists have since moved on to "academic freedom" and "criticisms of evolution" (which are still the same arguments as before).