For product results, you control whether the price and the product type appear on each card. The two controls live in different places, which is easy to miss.
Show price
The Show price switch appears in two places that do the same thing: the Configure step and Settings > Products ("Show price on results"). Both change the same setting, so the last one you save wins. Turn it off for quote-based or B2B catalogues. Price only shows when the product actually has a price.
Show product type
The Show product type on results switch is in Settings > Products only, not in the Configure step, so look there if you cannot find it. It shows the product's category on the card, and only when the product has one.
What always shows, and the out-of-stock marker
Every result shows its title and a short snippet. A thumbnail shows when the item has an image.
The Out of stock marker is separate from Show price: it appears on an out-of-stock product even if price is hidden. Whether out-of-stock products appear at all is a different setting, covered in its own article.
In the full-page layout, hiding price or product type also removes its filter from the side rail.