No, computer engineering tends to focus more on hardware. When I was doing that kind of thing in college, computer engineering did things like chip design and logic boards and so on. I had courses on DSP and VLSI, multiple assembly languages, RISC vs CISC systems, and so on. In my university, it was considered a subspecializqtion of electrical engineering, with the first two years of undergraduate study being identical.

When I switched over to CS, I was doing things like numerical analysis and software systems architecture.

Both majors used math, but CE (as an EE major) required students to go through (iirc) calculus 5, and I think that CS majors could stop at calc 3 but would end up having to do different kinds of math after that.

Think of it more like programming without electricity.

No, the machines tend to be abstract. Such as an infinite paper tape that can manipulate symbols.

No, that's machines with math