Classic means of enduring quality, or typical of its kind — a classic novel, a classic mistake. Classical relates to ancient Greece and Rome, or to established formal traditions: classical music, classical architecture, classical physics. A classic car is admired; classical studies concern antiquity.
The core difference
One is a judgement of quality; the other names a tradition or period.
- classic — exemplary, or archetypal: a classic design, a classic error.
- classical — of antiquity, or of a formal tradition: classical Greek, classical music, classical mechanics.
The technical uses
Classical does real work in several fields. Classical physics means pre-quantum physics; classical music means the Western art-music tradition (and, more narrowly, the period between Baroque and Romantic); classical conditioning is a specific psychological mechanism. In each case it means "the established framework", not "excellent".
The trap
"A classical mistake" reads oddly, because classical does not mean archetypal. The idiom is a classic mistake.