> No company is a what it actually does company.

Or perhaps that companies, like individuals, have facets.

Someone calling Google a search engine company is no more correct than you saying they are an advertising company, technology company etc, or in a negative sense, a monopoly.

Each of these epithets refer to the same entity, it's just that each emphasizes a particular trait over other traits for the point being made. A regulator is more much more likely to use "search engine" in conjugation with "monopoly" to characterize Google than with the term "technology company" since their goal is to highlight a potential case of abuse that is known to stem from such market power.

True, but I'd phrase it as "no big company is actually a what-you-think-it-is company."