There seem to be four different Latin words, all of which are common, and all of which seem to mean exactly the same thing, "finally":
Is there any difference between these words, or are they all interchangeable? Seems kind of ridiculous to have have four adverbs all meaning the same thing.
I would say, in a sense, tandem is little different from the rest, as tandem tends to imply pressure that was accumulating and being released, or something that was expected and finally happens (i.e. Not necessarily after sequence of events). Thus, you can see tandem used to intensify a question to indicate asker's stress. Practically speaking, in the title of this question: "Can we finally know the difference between these words?" I would gladly translate finally as tandem - and it seems others are less appropriate.
At any case, they are all indeed very close. To reveal the nuances, it is adviced to consult some good books of Latin Synonyms like this of Dumesnil, that I'll quote here:
DEMUM, at length, after a long time. Nunc demùm litteris tuis rescribo. (Cic.) Demùm is also taken in a sense analogous to solùm, tantùm, only. Ea demùm magna voluptas est, æqualem ac parem verbis vitam agere. (Cic.) —DENIQUE, in fine, is placed at the end of a long enumeration. Non avaritia, non libido, non amœnitas, non nobilitas urbis, non deniquè labor, &c. (Cic.) —TANDEM, when a thing has been a great while longed-after. Tandem progreditur magnâ stipante catervâ. (Virg.) Ibis tandem aliquandò, quò te, &c. (Cic.)
