What's the difference between classical and classic? Should we say classic content in textbooks or classical content in textbooks?
First, we should look at the definitions (from Google)
Judged over a period of time to be of the highest quality and outstanding of its kind
- a classic novel
- a classic car
(of a garment or design) Of a simple elegant style not greatly subject to changes in fashion
- this classic navy blazer
Remarkably and instructively typical
- I had all the classic symptoms of flu
Of or relating to ancient Greek or Latin literature, art, or culture
(of art or architecture) Influenced by ancient Greek or Roman forms or principles
(of language) Having the form used by the ancient standard authors
- classical Latin
Based on the study of ancient Greek and Latin
- a classical education
(typically of a form of art) Regarded as representing an exemplary standard; traditional and long-established in form or style
- a classical ballet
Of or relating to the first significant period of an area of study
- classical mechanics
Relating to or based upon concepts and theories that preceded the theories of relativity and quantum mechanics; Newtonian
- classical physics
In both cases there is a sense that classic/classical relates to something typical or held in some kind of esteem (classic cars are outstanding, Greek and Latin are considered important and prestigious to learn). However, classical is used to describe things that are much older than things which are merely "classic". Classic Rock music is from the 70s while Classical music is from centuries ago.
In the case of a textbook, it would depend on the contents of the textbook, such as whether the textbook is describing something with a long tradition (classical algebra) or whether it is a particularly well-written example fondly remembered by the students who used it (a classic text about algebra).
The adjective classic is defined as 'exemplary of a particular style' or 'exhibiting timeless quality'. For example, a 'classic car'.
The adjective classical, in the sense you describe regarding textbooks, means 'of or pertaining to established principles in a discipline'. For example, 'classical mechanics'.
So to answer your question, 'classical' would be the word to use.
‘The Cambridge Guide to English Usage’ has a good article on this. Here’s an extract:
While classic has become a more popular and subjective word, classical maintains the higher ground. It is suffused with a sense of history and great artistic traditions: classical music is associated with a period of outstanding music in western Europe in C18 and C190; and classical ballet embodies what for many is still the acme of balletic technique, developed last century.
The article goes on to consider the use of classy, concluding that:
Classy is more direct and down-to-earth however; so it can probably coexist with classic for some time to come.
(FWIW, I like to think of music being divided into formal and informal, rather than classical and popular.)