That is a good question. At first it seems the 2 words can be used interchangeably, as they are both adjectives, but the first references for "classic" in the dictionary are as follows:
Classic
1. from the first or highest quality, class, or rank, such as 'a truly classic piece of work';
2. serving as a standard, model, or guide: 'the classic method of teaching arithmetic.'
3. of or pertaining to Greek and Roman antiquity, esp. with reference to literature and art.
4. modeled upon or imitating the style or thought of ancient Greece and Rome: The 17th and 18th centuries were obsessed with classic ideals.
Conversely, the references to "classical" are as follows:
1. of, pertaining to, or characteristic of Greek and Roman antiquity: classical literature; classical languages.
2. conforming to ancient Greek and Roman models in literature or art, or to later systems modeled upon them.
3. marked by classicism: classical simplicity.
4. Music.
a. of, pertaining to, or constituting the formally and artistically more sophisticated and enduring types of music, as distinguished from popular and folk music and jazz. Classical music includes symphonies, operas, sonatas, song cycles, and lieder.
b. of, pertaining to, characterized by, or adhering to the well-ordered, chiefly homophonic musical style of the latter half of the 18th and the early 19th centuries: Haydn and Mozart are classical composers.