Is this for logic? A tautology is a logical truth. It is true for all substitutions of its variables. A theorem is a statement deduced from the axioms of the system, and from other theorems and tautologies.

Tautology: a = a
Theorem: a + b = b + a (= c)

Thinking of Godel, the tautology is the inherently unprovable statement that allows completeness, that is, it's an axiom. To Kant (if I'm reading the Prolegomena right), a theorem can be presented in two ways: a + b = b + a (analysis or restatement of subject in predicate) or a + b = c (synthesis or the predicate being a wholly different concept derived from the subject). For example, the statement A line is the shortest possible distance connecting two points is a tautology (Euclidean axiom) whereas the statement A line is a sequence of points extended in one direction is a theorem based on said tautology (note lines can be either finite or infinite).