I know there are various clients, but is it possible to access my home Mac remotely via open vnc://... from the terminal? I can do this with my work Mac, which has a dedicated public domain name. However, my home Mac just has its local IP address, so I’m not sure how to access it when away from my home network.
Generally speaking yes, however VNC is not an especially lightweight protocol and depending on bandwidth and what you are trying to do may not be the best performaing answer for remote control across the internet.
The other problem is that, like you pointed out, your work PC has a dedicated public domain name making it easy to get to it from anywhere in the world (essentially). To do the same with your home PC you have to, for all intents and purposes, give it a public domain name.
there are a number of companies that can do this. The one that springs to mind is https://dyn.com/dns/. I have no affiliation and have never used it. But it is designed to give a device with a dynamic IP address (as most home routers are) a host name. This usually requires a router with support for such a service, so you will have to log into your router and check and see if it offers compatibility with this kind of service.
Once you have that set up you then have to forward the correct TCP/IP port from the router to your Mac at home and verify that your Mac at home is set up to receive VNC connections.
W H E W
Personally I would just use a service like LogMeIn, TeamViewer or any one of the dozen or so services (free, cheap and otherwise) that bypass all that networking setup and expense by installing a client on the target Mac (or PC) and accessing it via a web browser or a lightweight app.