Use alphabetical to describe things that are in order according to the letters of the alphabet. Use alphabetic for of or relating to an alphabet.
Alphabetic and alphabetical share the sense arranged in order according to the alphabet, but alphabetical is far more common in this sense. In current English-language news publications with content available online, “alphabetic order” appears only about once for every 2,000 instances of “alphabetical order,” and this ratio is roughly borne out through other types of writing.
The words do differ slightly, though. For the sense of or relating to an alphabet, alphabetic is more common. This is a relatively new development. The forms were interchangeable in all their senses before the second half of the 20th century, though alphabetical was more common. In the 20th century, however, the flourishing of linguistic studies gave rise to the newer, unshared sense of alphabetic. That differentiation has stuck, especially in scholarly and scientific contexts.
Alphabetical, as used in the following examples, is the preferred form for the sense arranged in order according to the alphabet:
This encyclopedia has meaning beyond its alphabetical entries and thorough cross-references. [Chicago Tribune (2012)]
[T]he listing of authors in alphabetical order affects the careers of those whose names begin with letters towards the end of the alphabet. [Social Studies of Science (1977)]
In addition, the adoption of a strict alphabetical sequence tends to separate periodicals dealing with the same subject, which a ‘catchword’ method tends to bring together. [Nature (1938)]
Alphabetic, in modern English, tends to mean of or relating to an alphabet—for example:
But most studies of the condition have focused on letter-based, alphabetic languages such as English. [BBC (2004)]
Next, the recipient would need to know the correct alphabetic code. [Scientific American (2012)]
The articles in this special issue share a concern with the role of morphological skills in the learning of alphabetic orthographies. [Reading and Writing (2000)]