Statistical AI, arising from machine learning, tends to be more
concerned with "inductive" thought: given a set of patterns, induce
the trend. Classical AI, on the other hand, is more concerned with
"deductive" thought: given a set of constraints, deduce a conclusion.
Another difference, is that C++ tends to be a favourite language for statistical AI while LISP
dominates in classical AI.
A system can't be truly intelligent without displaying properties of
both inductive and deductive thought. This lends many to beleive that
in the end, there will be some kind of synthesis of statistical and
classical AI.