Suggested answer:
(1) Classical is slightly more common than classic in the corpus, with 177 vs. 106 occurrences.

(2) Examples of classic and classical where they have similar meanings:
The classic example of this was William Marshal...
...the classical example is the pin factory eulogised in Adam Smith's...

Here both classic and classical have the meaning of "definitive/typical".

Examples of classic and classical where they differ in meaning:
It is a gorgeous, classic Bentley.
Surviving materials from the classical world of Greece and Rome...

In the two examples above, classic has the meaning of "of the highest class/first-rate", while classical has the meaning of "relating to ancient culture" (particularly Greek and Roman).

(3) Classic can also be used as a noun. An example from the corpus is:
...Walter Ash said it was a classic...

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Read about adjectives ending in -ic and -ical here
Terminology: adjective, noun