I am trying to gain a deeper understanding of logic, especially proof theory in its many forms, and I am curious about the common use of the term "Logic". It is often confusing what the precise semantics of "logic" are in any isolated reading of the many descriptions of the topic area. For instance, the term "Propositional Calculus" and "Propositional Logic" are sometimes used interchangeably. Confusing things more, "Propositional Logic" and "Classical Logic" are used interchangeably.
From what I can intuit, it seems that there are a few popular logics; Classical, Intuitionistic, and Linear. Each with differing definitions of the semantics of truth and falsehood. Then there are algebras for logic; propositional, relational, first order, and second order. Lastly (at least for the distance i am currently willing to travel) there are proof calculi; sequent calculus, natural deduction, and axiomatic (i.e. Hilbert style).
Am I way off here? Are there any resources for clarifying this (please don't reply with wikipedia because that is causing some of the difficuties)?
Thanks in advance.