The "formal" in "formal argument" does not mean "the opposite of casual". Rather, it refers to arguments which take a particular form: those that assume a set of premises, and use formal logical tools to prove a conclusion from those premises. To accuse an argument of containing a formal fallacy means: the tools you tried to use to prove that conclusion from those premises is defective, and you have not actually proven the conclusion.

However, proving a conclusion is only one possible thing that an argument may set out to do. Oftentimes, we are more interested in probabilistic evidence than in absolute proof. Thus, an argument which does not prove anything (and which would thus be fallacious if treated as a formal argument) can nonetheless be useful.