It might be that I don't see how what you classify as Product A and Product B are different products. I see Product B as the monetization feature of Product A. If I "squint" I can see how they are different products but I am not convinced.
Product B is display ads, which are displayed on other (almost always non-Google) websites. No searching involved...
I don't see how they're even remotely the same product. They're similar in the sense that their forms of advertising, but they're very different forms of advertising. Search placement is intentional advertising (in the sense of targeting prospective customer's "intent" to use/buy) while display ads are awareness advertising. The proof is in the very different rates: search engine placement terms can cost several dollars per search. That same amount could buy hundreds or even millions of display impressions.