Yes, but you need two separate profiles. Please read Profiles - Where Firefox stores your bookmarks, passwords and other user data.

Firefox is based on a model of local data storage that you can synchronize between installations using a Firefox Account. It is NOT based on a model of a temporary instance of a cloud browser that disappears when you log out of your Firefox Account. This is key to understanding how to set up what you want.

What are Firefox profiles?

A Firefox profile is a pair of folders that store browsing data such as bookmarks, logins, add-ons, cookies, and cached files. You can have multiple profiles for different purposes and launch them from the about:profiles page. That is also where you can designate one to be your default to handle external links. If you are changing hats throughout the day, you may be switching the default a couple times if external links and shortcuts need to be directed to a specific profile.

What are Firefox Accounts?

You can create one or more Firefox Accounts, but each must have a unique email address. You can log any profile (and any number of profiles) into any Firefox Account, which allows combining data among all the profiles connected to that account. This is how to mix up your carefully siloed data if you aren't careful. Since you want individual silos, you should not log into a Firefox Account used for one silo while using a different profile.

Bottom line: the profiles are the main thing, while accounts connect you to services your profiles can use.

If you want (have) to keep data separate and only have one home device and one business device then there is no need to use Sync and there isn't another device to sync to.