This is maybe more obvious in hardware design.
At the top of the tree you have people like Maxwell, Heaviside, and Shannon, who invent entirely new possibilities out of pure math.
At the other extreme you have technicians who don't truly understand math or theory, but can build a circuit that will probably work if handed a cookbook.
In the middle are people who can work with abstractions like DSP and filter design as long as the ground has been broken for them. They understand enough math to find their own way through a problem from first principles, but aren't creative enough to invent anything truly original.
CS is more amorphous, the levels are maybe harder to separate, and it's cursed by not having a truly consistent practical mathematical foundation analogous to the applied physics that underlies engineering of all kinds.
But IMO there are similar skill levels - although at the higher levels, abstraction can become a bad thing rather than a good one.
The problem is that although there's math in CS, after Church/Turing - which is pretty elementary compared to most physics - there isn't anything that passes for a formal theory of problem/solution specification and computation.
Without that objective basis, a lot of CS is academic opinion instantiated in a compiler. And a lot practical commercial CS is a mountain of hacks built on language and tooling traditions with no empirical foundation.
Commercially, the most productive people will be middle-rankers - not so clever they'll be thinking of new applications for category theory in an iPhone app, but clever enough to be able to think beyond cookbook development.
Now, in other areas, we have a distinction. We have physics departments that teach people theory, and we have separate engineering departments that prepare people for careers putting the theory to useful work. Well, where does the CS program live? At least where and when I went to college, the CS program was part of the Engineering department.
So I think it's fair to say that colleges should take on considerably more of the job of preparing software engineers for real-world careers in software engineering. Hiding behind "we teach CS, not software engineering" is a cop-out, especially if CS is within the College of Engineering.