It's more different than you think because there are many permutations of search terms. There are products that rank really well for odd phrasings of a product search term but not well for the most popular variations. There is also virtual shelf space for weird, niche items with additional features that are not that popular. Amazon aggregates hundreds of thousands of small businesses globally and also tailors search results to FBA warehouse availability. So for example if the warehouses near you are well stocked with product A and not product B you will see product A ranked relatively higher than product B would if you are a prime subscriber, but you will get neutral results when logged out or a non-prime subscriber.

Then you throw in Amazon Shopping ads (aka Sponsored Products) and the shelf space metaphor gets muddled further, because it's like as if every store visitor saw unique and different endcap displays and shelving ordering. There is less individual tailoring to search results than you might expect on Amazon (especially compared to information search engines like GoogleBingBingGo) but it is still a factor.

Then there is the factor of endemic counterfeiting in some categories, so the sketchier the listings are the more likely you are to just buy a counterfeit product, which would never happen in a typical brick and mortar retail shop.

IMO Amazon's private labels are so minor and make up such a small portion of store sales that it ranks very low on the scale of things that Amazon does that are morally/legally questionable.