I’ve been doing the secretary/assistant thing for longer than I care to admit, so I probably know something about this.
For the most part, administrative assistants (that seems to be the curent collective term) do not run personal errands, get lunch, or get coffee for people.
I did have one job once where, in the interview process, it was made clear that part of my job was to make coffee for the office. Which I was OK with, since it was mentioned up front with all the other job duties and I could factor that into my decision whether or not to take the job. I mean, if you want to pay me to make coffee OK, I’ll do it.
These days, at least in Chicago, it would be seen a pretentious and arrogant to have someone get your coffee for you. The exception would be guests of our company, where I might offer to get them coffee. Even so, most people prefer simply to be shown where the coffee is and pour their own.
For people under the executive level, the only time I would get lunch is if the whole office was ordering out that day. However, that duty is not automatically mine - quite frequently, someone else does pickup duty. Folks will offer to get lunches for each other “Sally - I’m going to get my lunch, can I get you anything?” - but that has nothing to do with business.
Executives do, occassionally, have their assistant get their lunch. It’s very rare where I work, and it’s usually on a day where the executive is overwhelmed with work and meetings. (I have, no joke, had to schedule bathroom breaks into an executive’s day) Personally, I have no objection to ocassionally getting a salad or sandwhich for someone working a relentless 10 or 12 hour day. Corporate custom, at least where I work, is to then buy the assistant a small token of appreciation (Starbuck’s giftcards are currently the norm, or even taking the assistant out to lunch at a later date. Because I’m known to be quite the reader, I also get giftcards to Borders from time to time). So, it does occur, but it’s recognized as a little above and beyond the norm and there is compensation for it. Doing things like fetching the dry cleaning is less common because many such places will deliver if you ask them to, so the assistant can stay at her/his desk doing their job instead of running such errands. The higher up the hierarchy the boss, the more likely you’ll be doing this sort of thing, but then the higher up your boss the more likely you are to extremely well-paid. Upper end executive assistants can make $70,000 a year in my area, but boy howdy, you’re going to work for it!
If you were asked to get lunch, or the dry cleaning, or pick up the boss’s kid and got in an accident - yes, it could come under worker’s compensation which is why my current company has strict guidelines about such things. Getting lunch is one thing - we all have to eat - but the other two would be quite questionable according to our company’s lawyers. It ain’t gonna happen where I currently work.
Of course, there are also arrogant jackholes for whom yanking another human being around and treating them like a personal servant is a complete ego trip. I avoid working for such people.