The textbooks are quite varied. There is not a "National" textbook. 

Books may be chosen from the School District,  the School itself (especially if private school). The county, etc.

By AP I assume you mean Advanced Placement? Not all schools have it but those that do, usually have it in most High School subjects (though there is NO AP class for Home-Ec).

Yes, textbooks are varied, it's a competitive market.

AP classes vary by school too (bigger/richer schools offer greater variety of classes).

I can tell you from what I remember my school offered AP A/B Calculus, Biology, Chemistry, Physics, US History, and World History for sure.  I know they offered more, but those are the ones I can specifically remember.  

I believe they offered some sort of AP English and AP foreign languages (from Spanish, French, Italian and German), but can't specifically remember anyone who did.

I've also worked in another larger school that offered AP Statistics.

Most of the text books will only last a couple of years and they usually replace it with other books the newer version which is slightly different. It's kind of like college after a couple years they usually revise the books that way they can make new books and sell them to students. 

there is not a national textbook in America high school. Here is a website about AP http://apcentral.collegeboard.com/apc/Controller.jpf