The taxonomy I personally use is:

* Every computer program has algorithms, it's an extremely general term for "the idea behind how the computer will solve the problem". Advanced algorithms are typically those that took a lot of human effort to come up with.

* Machine Learning refers to a specific class of algorithms where the computer automatically figures out (part of) what it should do based on data.

* Deep learning is the subset of ML that uses deep neural networks.

* Artificial Intelligence is a marketing term, and is actually about the _problem_ being solved, not the technology being used to solve it. In particular, AI is any computer program that solves a problem people would previously expect can only be solved by a human applying creativity and/or intelligence, like playing a game, understanding natural language, or creating artwork. This definition is obviously a moving target as expectations change.

Deep learning is currently the most powerful and general toolkit for solving AI problems, so the concepts tend to get mixed together pretty frequently, but I personally like using the definitions above to keep things straight.

I like your taxonomy. But just to clarify: is the cruise control on my car "artificial intelligence?" Because a lot of dumb 15-year-old teenagers don't know they have to increase power while going up a hill, while my cruise control algorithm does.

My category for AI is based on "popular perception", not necessarily an actual comparison to what humans can or can't do. Most humans don't know how to multiply complex numbers, but that doesn't mean doing so demonstrates human-level intelligence and decision making.

In the specific case of cruise control, I don't think maintaining speed accurately is typically viewed as "difficult" for a computer today, so it would be deceptive to refer to as AI. 100 years ago that may have been different.

I like your framework.

Would you put statistical analysis "algorithms" in the same category as "Machine Learning"?

Sure, "classical" ML of various forms (knn, decision trees, etc.) are Machine Learning, but aren't Deep Learning. That's exactly why the distinction between those phrases is useful.

Clearest and most useful descriptions I've seen by far. Thanks for sharing

It just sounded like a good description. We never got any funding and started the business as a side project so no need for big words :)

Algorithms are provably correct. If you've got no proof of correctness, the best you have is a heuristic.

Depends on whether you use the traditional or vernacular definition of AI. Traditionally it was more about the how not the what. AI was an agent acting rationally in an environment. Pac-Man guided by Dijkstra? That's AI, there's an agent, an environment, and said agent is acting "rationally".

In modern vernacular it has become a synonym for machine learning or sometimes specifically neural networks.

The amount of VC funding you'll get.