But why is Google successful at selling ads? It's because they're best-in-class with AI techniques. Google's revenue is from ads. Google's technology/core competency is AI. Classifying companies is hard, and it doesn't really make sense to try to fit your worldview into "X is Y, A is B". Sometimes X and Y are both A and B.

That makes sense only if you view companies as abstract money generating entities stable over time. In case of Google, it matters more what's their primary competence (information technology) and goals (information technology, solutions to big problems).

Couldn't you say they were a big data company as well? It seems that all that consumer data is what makes them such an effective ad company.

I would say their goal to sort and organize the world's data is right in line with their existence as an AI company. You're not wrong at all that they make tons of money in ads, but then that is also significantly understating the role of communication and Google's role in communication these days.

But the big data is essentially just the knowledge base for the AI.

Yeah, but Google did a huge marketing push that they're an "AI company" recently because that sounds a lot more scifi than the reality that Google's primary revenue stream isn't that different from a company that does cold calls. Marketing isn't exactly appealing to consumers. ;)