I would call it "software engineering" personally, but "computer engineering" is adequate, and it has a nice parallel to "computer science". But yes, I think they're distinct, as distinct as chemical engineering is from chemistry.
In chemistry, they worry about the properties of individual atoms, and how those atoms combine to form molecules, and how much energy that takes or gives off, and where the electrons distribute themselves in the molecule, and how that affects the properties of the molecule. In chemical engineering, they worry about how to efficiently make this stuff in multi-ton quantities without blowing up the city, and cost of raw materials, and disposal of waste products, and things like pipe bursting strength. Yeah, they'd better know some chemistry, but they need to know a lot more than that.
In the same way, computer engineering or software engineering is about the efficient construction of larger-scale programs that adequately meet the need they are written to address. Let me unpack parts of that definition.
"Efficient": Well, that's actually a bit of a lie. What I should have said is "somewhat less inefficient", but my description was already long enough. But large scale software construction is inefficient, and the larger it is, the more inefficient it is. The fundamental reason is that brain-to-brain transfer of information is lossy. The bigger the program, the more brain-to-brain transfers involved.
"Larger scale": There's something called the "rule of 10", that says that for every factor of 10 larger the program gets, a new set of problems comes to predominate. You still have at least 10 times as many of the old problems, but you also come to have new problems. On truly large programs, the biggest problems may be transfer of knowledge between generations of workers.
"Adequately meet the need": I didn't say "bug-free". Larger programs have bugs. They have databases just to keep track of the bugs, and steps to reproduce them, and to decide which ones to bother fixing, and to figure out who (or at least which team) should fix them.
I'm not sure that many CS degrees to much at all to prepare people for any of this. But I suspect that 90% or more of people with a CS degree are going to wind up working as computer/software engineers rather than as computer scientists, and so I suspect that there's a mismatch between education and career here.