Evolution is a process. (“Descent with modification.”) Natural selection is a mechanism which supposedly accounts for the process.
Evolution might take place for a combination of reasons, including a number of natural processes, and also possibly including intelligent direction or pre-planning.
Natural selection (and by extension other “undirected processes”) is opposed only when it is understood that natural selection (or natural selection plus other “undirected processes”) is the exclusive cause of the process of introducing new species.
Thus, Behe can grant that natural selection, and mutation, and other things, do play a role in generating new species, but that something else – design – is also involved. He is classed as an ID supporter because of his insistence on design. Jerry Coyne, on the other hand, insists that design is not involved, so he is not an ID supporter. Both are “evolutionists” in that both believe that species have been modified over time to become new species (i.e., there is genetic continuity between the new species and old), but Behe, in addition to being an evolutionist, is a design proponent, whereas Coyne is an evolutionist instead of a design proponent.
So the opposition is not between design and evolution (where evolution is understood as a process involving descent with modification), but between design and entirely undirected causes of biological change.
This leaves ID as a group which is internally divided regarding notions such as descent with modification, common descent, universal common descent, etc., since these notions can be retained or jettisoned within a design perspective.
If you remember your Venn diagrams, you could draw two circles, one representing “evolution” (defined as “descent with modification”) and one representing “design”, and there would be an overlap zone whether the two circles intersected. In the overlap zone would be all ID people who accept common descent to a significant degree, e.g., Mike Behe and Mike Denton and, depending on how you interpret certain statements, possible Rick Sternberg, and, perhaps in the past and maybe even now, Ann Gauger, as well as many lesser-known folks (such as Dave Scot who used to moderate UD).
Outside of the overlap zone, the “design” circle would include creationists, both Old and New Earth, and the “evolution” circle would include those who understand undirected processes to be entirely sufficient to explain all organic change (Coyne, Dawkins, Myers, Harris, Krauss, etc.). Thus, Ken Ham would be outside the overlap zone within the design circle, and and Dawkins would be outside it within the evolution circle.
The evolutionary creationists of BioLogos and the ASA are harder to diagram; one would need two different Venn diagrams for them, a “science” Venn diagram and a “theology” Venn diagram. In the “science” Venn diagram there would be no overlap between the circles, but in the “theology” Venn diagram there would be. This oddity is required because the ECs claim that they believe in design when wearing their theologians’ cap, but not when wearing their scientists’ cap. When wearing their scientists’ cap, they treat evolution as occurring wholly due to natural processes, and, given the way they understand “nature” within the enterprise of natural science, that means undirected natural processes (undirected as far as science can now or could ever determine).