My action lists are combined. I use index cards, and my contexts are:
-home office
-home other
-workplace
-grocery store
-drug store
-other errand
-phone
-internet
-computer

So, the handful of things I only can do at home or at work get separated out, but I'll often have both work and home things on my phone, errand, internet, and computer lists.

I think it really depends on the kind of work you do. I'm in a small nonprofit doing community development work, and the lines often feel fuzzy. I mean, if I have to go to an office supply store to buy supplies for work, it would feel insane to not also pick up a refill for my home labeler, if that's what I need.

If your work can only be done at work, and your bosses aren't flexible about you doing things for home on work hours, then it would make sense to split the two sets of lists.