I've served a whole bunch of roles in my five years at my current employer, and I'd probably classify myself as being an "electrical engineer" for all of them. (No single experience is typical, but mine is probably representative of a lot of chip companies.)

When I joined the company, the very first role I was put in was on the core bringup team for a complex ASIC -- that is to say, the team responsible for screening chips, and working on issues that affect all of the individual functional blocks. I joined about a month or two before silicon was to come back. So, I spent the first six or eight months or so at the company in the lab; the first month was spent familiarizing myself with the tools and boards that we'd be using, and then once silicon came back, I spent a bunch of long nights and weekends in the lab getting chips to various teams, and, in general, solving whatever system-wide problems showed up. Bringup was a lot of work but it was also a really good view into "how the sausage was made", so to speak.

After bringup, I moved to an IP team [1], where my title was "ASIC Engineer". At the phase in the project that we were in, most of the RTL [2] had already been written, and owners for each sub-block had already been assigned. So my job was to do a bunch of the "checklist" items for netlist quality. For instance, I spent a while reviewing test coverage, and waiving coverage for things that couldn't possibly ever be reached. Or I reviewed tool output that did "clock domain crossing verification" -- basically, the tool pattern-matched on various chunks of code to make sure that they were safe. And yes, I spent some time staring at waveforms, trying to debug our testbench, or any kinds of such things.

I spent a while on another couple bringups, which I volunteered for this time. I enjoyed them, and then gave myself some time off for each to compensate myself for my nights and weekends.

At some point, someone decided that I was a better architect than engineer, which is probably for the better, because I was very slow at checklist items. So at some point I switched to an architect role, which meant that I was responsible for doing the definitions of sub-units, rather than implementing the hardware for them or implementing the testbenches for them. And, in general, the whole specification process is part of the architecture team's job. So, one day, when there was an output quality problem with our block -- it worked as specified, but given that it did some image processing, the image quality had some defect, so the specification was wrong -- I was tasked with spending a few weeks to reproduce it on hardware, find register settings that made it better or worse, and finally, understand what the defect was in the specification, and how to avoid it in the future.

Another task I had as an architect was to do the definition for a sub-unit from the ground up. This was a year or two of work. My primary output, interestingly, was not code, but instead a 100-or-so page Word document that specified how the block was to work, and what registers should program it; the consumers of that document would be the hardware team that implemented it, and the software team that would build the software. And, subsequently, I was tasked with implementing a model of that block in C, which could be checked against the RTL that the design team wrote. Near the end of that project, I wrote validation tests for it, and yes, I then spent some time staring at waveforms helping the design team to understand why their RTL implementation diverged from my C model. (They were, often, right. I am very lucky to work with an extremely skilled RTL team.)

These days, I'm doing more algorithmic research, trying to figure out what should be next for the block that I'm working on. In parallel, I sometimes get on phone calls with, for instance, image sensor vendors, understanding on an electrical level what's going on inside of their next sensors, and how they will be transmitting data back to our processor. So even though I work in the digital domain a lot of the time, having a firm grounding in 'is it possible to wire this to this' has gone a long way to help out, and being handy with a soldering iron has made my life a lot better on more than one occasion.

My experience spans some gamut, but not all of it. I don't work on place-and-route, and I don't work on board design (at work, at least). There are a lot of things that electrical engineers do :-)

Hope this helps. (I can answer questions, I suppose, if you like.)

[1] For some reason, the semiconductor industry calls functional blocks IPs -- yes, as in 'intellectual property'. This particular IP was not something that we licensed to anyone, or that we licensed from anyone; the only 'customer' of this IP was our own chip team.

[2] Again, another acronym whose expansion ("Register Transfer Level") is not super descriptive. Essentially, source code. Usually in Verilog, or an even higher level language. EEs seem to love Perl and Tcl, so most places I've worked have had Perl or Tcl preprocessors before their Verilog. Ugh.