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Arguments can be logical or rhetorical.

Logical arguments are those which determine whether a particular statement is true or false.  Rhetorical arguments are those which attempt to persuade a person or audience that a particular statement is true or false, regardless of whether it actually is true or false.

Logical arguments attempt to determine whether a particular concept or category is inside or outside of another category.  e.g.  Is A inside or outside of category B.  This is achieved by defining A and B sufficiently enough for the laws of logic to make the answer clear.  If A and/or B cannot be sufficiently defined, a logical argument is concluded without an answer.

Rhetorical arguments attempt to persuade someone that A is inside or outside of category B, prior to A and B being defined sufficiently to form a logical conclusion.  This is achieved by means of asserting evidence which is designed to affect probability judgment.  The opponent is expected to either admit that the evidence is sufficiently persuasive, or challenge it (or parts of it), or offer counter evidence.  Each challenge or piece of counter evidence is expected to be reciprocated likewise.  Counter evidence may or may not address the evidence previously presented.

Logical arguments proceed directly from premises to conclusion.  Rhetorical arguments can proceed in multiple directions simultaneously, and can be protracted indefinitely.  Such an argument ends only when one of the parties gets sick of it.  Anyone looking for a logical conclusion can save much time by recognizing such an argument as a pissing contest as soon as the opponent refuses to define relevant terms.

The above is not an argument.  If it were, I would have defined logic and rhetoric.