A rather interesting use case, and one that I haven't been forced to deal with just yet. On a rather cursory search, however, I came across Switchy: https://addons.mozilla.org/en-US/firefox/addon/switchy/

Are these two solving the same problem?

Managing different profiles is a use case that has basic built in support by running `firefox -P`, however the article talks specifically about how to automatically send certain links to different profiles without you doing anything but a regular click.

Which it seems is precisely what this addon solves.