What are the differences in scope between statistical AI and classical AI?
Real-world examples would be appreciated.
Statistical AI, arising from machine learning, tends to be more concerned with inductive thought: given a set of patterns, induce the trend.
Classical AI is the branch of artificial intelligence research that concerns itself with attempting to explicitly represent human knowledge in a declarative form, i.e given a set of constraints, deduce a conclusion.
Another difference is that C++, Python, and R tend to be a favorite language for statistical AI, while LISP and PROLOG dominate in classical AI.
A system can't be more intelligent without displaying properties of both inductive and deductive thought. This leads many to believe that, in the end, there will be some kind of synthesis of statistical and classical AI.
Machine learning techniques are usually using a lot of statistical approaches, like neural networks: a book like this one (Understanding Machine Learning: From Theory to Algorithms ISBN 978-1-107-05713-5) is full of mathematical equations.
Symbolic artificial intelligence, e.g. classical expert system approaches (with some knowledge base), is more related to logic: a book like that one (Artificial Beings: the Conscience of a Conscious Machine ISBN 978 1848211018) has mostly no complex equations, but simple ones.
Artificial neural networks are somehow "working", but you cannot understand why.
Knowledge-based systems are more explainable artificial intelligence.
Classical AI systems could generate code (in C, C++, Common Lisp, machine code) using metaprogramming techniques, and could be mixed with machine learning or deep learning approaches, and/or use existing machine learning libraries.
Notice that the difference between statistical AI and classical AI is not a matter of programming languages or of operating systems. For example, garbage collection may be (and perhaps is not) relevant to both approaches.