In Windows I use, beside the main Firefox installation, one or even two "Firefox clones" for different purposes (specifically oriented addons and configurations, light configuration without addons, configuration for a different user, etc).
For example, in Windows, Pale Moon, Cometbird and Wyzo are FF clones (but they do not have Linux support). Basically, Flock browser would also qualify, and it had support for Linux: but it was discontinued.
A "Firefox clone" is a term that I adopted from the use in Windows, the meaning of which includes these two elements:
(1). is a browser that is identical (based on Mozilla Firefox) or very similar and has large/full support for FF extensions, configuration, profiles. = can use FF extensions etc.
(2). runs independently from Firefox, can be opened at the same time with Firefox = does not share FF extensions etc.]
(That is, a FF clone would be to Firefox what Google Chrome and SRWare Iron are to Chromium - almost identical, but able to run separately in parallel.)
[Seamonkey, has support for Linux, but (although it can use a lot of FF extensions): themes are not working, the interface is in general different and rather primitive. It has the merit of keeping the pace with FF 4+ (in contrast with Swiftweasel, for example.)]
Are there such more browsers available in Ubuntu?
(As for comments asking why I "really" need these "clones", I am just used to doing that, I like two separate Firefox-like browsers: isn't pleasure, just like curiosity, a good reason for an action?)
Edit after using multiple accounts: after testing for a while this solution that has prevailed here (was most up-voted) of using multiple accounts I have to say that it may involve certain problems in cases where other separate customizations/advanced uses are implemented. (For example, using scripts to search internet for selected text may open new unwanted profiles instead of the default one; or using firefox "openwith" addon to try and open a link with a new ff profile would give a report that the profile is not accessible.) A complete separate browser for a parallel use may be in such cases more useful. (In this respect, Seamonkey deserves to be taken into account. )
Edit considering the definitive answer: although answers proposing the use of multiple accounts were most voted, I will prefer an answer that proposes a separate browser, for two reasons: 1. that is what the question asks for in the first place, and 2. multiple accounts may involve some problems, like those mentioned above.