Difference between "always use private browsing mode" and containers?
What's the difference in protections between "always use private browsing mode" and containers (multi- or Facebook)?
There is no comparison to make between the two.
It may be useful to know that a regular Firefox window caches web files and stores cookies on disk, and a private window stores that kind of data only in memory, and it is purged when you close the last private window.
These are two separate browsing contexts, for example, if you log in to your Google account in a regular window, and then open Google in a private window, the page in the private window isn't logged in because your Google cookies are not shared between regular and private windows.
You can of course clear cache and delete cookies in regular windows at any time or at shutdown, but if your browsing is so sensitive that you cannot even have it written to disk in the first place, a private window is useful. You also can set some of your add-ons to run in private windows and not others, which provides a way to access sensitive sites, such as your bank, with less exposure to possibly prying eyes.
Now, if you open a container tab in a regular window -- you cannot use containers in private windows -- that is a third possible context for cached files and cookies. This is useful if you want to use a site that has its tentacles everywhere (Facebook? Amazon?) and you don't want to be logged into your account in regular and private windows, only in the tabs in that container.
More containers = more contexts.
To have all this flexibility, though you cannot turn on automatic private browsing because then your Firefox is limited to one context, the private window world. Instead, you need to manage your contexts yourself by choosing what to open in regular, private, and container contexts.
Does that make sense?