They are actually the same thing! When people say Classical Greek, that is referring to Attic Greek. Attic is a dialect of Greek. ِAttic Greek is usually the first dialect that is taught in University as it is easier to branch off into other dialects from Attic.
It is great to learn first for the following reasons; lots of material to read and it easy to go off to other dialects later, its a great foundation. – Idea from page 3 of Introduction to Attic Greek Second Edition by Donald J. Mastronarde.