An inference is a movement of thought whereby a first set of thoughts leads to another set in a way that intuitively feels correct. A logical inference is a movement of thought that employs some sequence or pattern of symbols or representations, according to the rules of the model within which they were made or interpreted, so as to make sense of some additional object or subject or idea in an allowable or entitled way. The assessment of a logical inference is relative to the model used to understand it.
Arguments are inferences.
Sequents of wffs are representations of such inferences. We analyze and assess a sequent in order to judge the quality of the inference in the argument. Truth-table tests can show us whether a PropL sequent is valid or invalid. T-table tests cannot show us this. A derivation is a series of wffs that display HOW a sequent is valid.