"Allowing a site's cookies for Session" means those cookies won't be saved beyond the current session; they will be deleted as Firefox is being closed down.

With "Allowing a site's cookies" those cookies will be saved until those "time out" or until the user clears their cookies or until the user clears the cookies for that web site.

Note that you only keep cookies with a cookie allow exception if you use "Delete cookies and site data when Firefox is closed". If you use "Clear history when Firefox closes" or otherwise clear cookies then all selected cookies are cleared. In Private Browsing mode all cookies are session cookies that are removed when you close all Private Browsing windows (tabs).

cor-el said

Note that you only keep cookies with a cookie allow exception if you use "Delete cookies and site data when Firefox is closed". If you use "Clear history when Firefox closes" or otherwise clear cookies then all selected cookies are cleared. In Private Browsing mode all cookies are session cookies that are removed when you close all Private Browsing windows (tabs).

Just for clarification, you're saying that if I use "Clear history when Firefox closes" then all cookies, even if I set exceptions for some sites, will be cleared, is that right? What if, in the settings for "Clear history when Firefox closes", I unchecked "Cookies"? Can you confirm that, in this case, this won't clear the cookies from sites which have an exception?

Yes, if you uncheck Cookies and Site Preferences then you keep cookies with an allow exception.

• clearing "Cookies" will remove all selected cookies including cookies with an allow exception you may want to keep
• clearing "Site Preferences" clears exceptions for cookies, images, pop-up windows, and software installation and exception for password and other website specific data