Usually the second type is called “brand advertising”. The idea is to create a positive association with a brand and not expect you to take any immediate action. The first type maybe “action advertising” (I’ve heard other terms).
Assuming you mean "conversion advertising" vs "brand advertising", what I remember looking at industry-wide numbers when I worked on Google Ads was that they're actually pretty close, with brand advertising being slightly bigger. Something like 60/40 industrywide.
Now, it varies widely depending on the medium, search ads lean way more on conversion advertising, with display and especially video ads leaning more on the brand side.
Brands are bullshit. I'd actually be on board with the conventional capitalism view of producer-consumer information levels if brands went away. They distort quality, they distort product perception, they don't have anything to do with the actual reality of most people. “Consumption styles as part of personality” (aka brands) are a cancer.
Most advertising is actually the first type.