Full Idea
The point of logic is to give an account of the notion of validity,..in two standard ways: the semantic way says that a valid inference preserves truth (symbol |=), and the proof-theoretic way is defined in terms of purely formal procedures (symbol |-).
Gist of Idea
Validity is either semantic (what preserves truth), or proof-theoretic (following procedures)
Source
Herbert B. Enderton (A Mathematical Introduction to Logic (2nd) [2001], 1.1.3..)
Book Reference
Enderton,Herbert B.: 'A Mathematical Introduction to Logic' [Academic Press 2001], p.1
A Reaction
This division can be mirrored in mathematics, where it is either to do with counting or theorising about things in the physical world, or following sets of rules from axioms. Language can discuss reality, or play word-games.