What do "syntax" and "semantics" mean and how are they different?

A language is a set of valid sentences. What makes a sentence valid? You can break validity down into two things: syntax and semantics. The term syntax refers to grammatical structure whereas the term semantics refers to the meaning of the vocabulary symbols arranged with that structure. Grammatical (syntactically valid) does not imply sensible (semantically valid), however. For example, the grammatical sentence "cows flow supremely" is grammatically ok (subject verb adverb) in English, but makes no sense. Similarly, in a programming language, your grammar (syntax rules) may allow ID EQUALS ID but the language may only allow the sentence if the text matched for ID does not represent a type name (a semantic rule).

When you write an ANTLR grammar, you are specifying the set of syntax rules obeyed by your language. ANTLR uses this to generate a recognizer for sentences in that language. To apply semantic rules, you must add actions or semantic predicates to the grammar. The actions test the "value" of the various tokens and their relationships to determine semantic validity. For example, if you look up a type name in a symbol table to ensure it's a type not a variable, you are applying a semantic rule.

See the chapter on language in Terence's new (in-progress) book.