(updated June 20, 2018)
If you have two different computers (most commonly, a Mac at home and Windows at work), there are a few ways to handle this. None of them are thrilling.
Cross-platform apps: The seemingly obvious solution is to pick an app that can live in both places. There are problems with this: first, there are very few app options here, and you’re much more likely to fit yourself to the software than the reverse. Second, if your data lives on your company’s hardware, they legally own it, and can review it (or demand passwords) at any time.
Web apps: Usually preferable to native applications (in this situation only). Your data lives in the cloud, so no one at work can get to your database. But it has the same lack-of-options downside: web apps are less complex than native applications (usually; Salesforce is a major exception).
Run Windows on your Mac: There are several ways to run Windows software on your Mac. This actually works really well. The issue is, spoiler alert, Mac apps are just better across the board: more choices, better design. The how-to for this is a book on its own (and unfortunately, Take Control’s book about it is out of print), but here are the software names to Google to get you started: Boot Camp, Parallels Desktop, VMware Fusion, VirtualBox.
Run Mac on your PC, sort of: You can’t run Mac apps on a PC, but you can share the screen of your Mac at home. You see the screen on your Windows monitor, anything you type or mouse gets sent home, your Mac does the work and sends back the screen. It’s not perfect—there’s a little lag, and sometimes everything pauses for a few seconds if the Internet connection slows down. The main problem, though, is that you need to leave your Mac running at home to use it, and some tech wizardry is necessary to set up your home router. Get started here: how to share the screen on your Mac, and software you’ll need on Windows.
I think most people will be served best by a task app that runs on mobile hardware that they own. Run your task app on a tablet, and you can prop it up side-by-side with either computer, using pointers to make any organization use do on all three perfectly manageable.