> Google is an advertising company

Google is a company that sells space for ads; an “advertising company” conventionally refers to a company that designs ad campaigns and purchases ad space for them on behalf of a client.

> not a search engine.

No, its both. Just as historically newspapers publishers in the US have been both producers of newspapers and companies that sell ad space.

Google the company is an ad intermediary company. Google is also the colloquial name of Google Search.