Here, I'm going to talk about actives in the broader sense, so I'll discuss things that the FDA would categorize as a beauty product ingredient, not a drug—but will note when an active often falls under the FDA's definition, in the event you are curious.

Sunblocks, such as zinc oxide and titanium dioxide: These mineral actives fall under the FDA's purview—as they protect the skin from UV damage and the potentially dangerous side effects of too much exposure. They also have to be formulated at a certain percentage to be effective.

Antioxidants, such as vitamins C and E, astaxanthin, and CoQ10: Topical antioxidants do not fall under the FDA's regulations and thus will only appear on the ingredients list. However, they do wonders for your skin—by tending to wrinkles, inflammation, dark spots, and so on—so people often use them in skin care. Sometimes you'll see brands call out how much is in it (like if vitamin C is formulated at 20%, for example), but that's not necessary; it's only for marketing.

Salicylic acid: A tricky one, but this is often considered a drug—especially in the context of treating acne—so you'll often see it called out in an active label. However, some brands chose not to go this path and instead opt out of making "treating acne" claims and simply market their product as having it or will use the natural version, willow bark, in it's place. 

Alpha-hydroxy acids: These almost always are considered a cosmetic ingredient—and they work by gently exfoliating the skin. Common examples are lactic and glycolic acid.

Benzoyl peroxide: This antibacterial agent is regulated by the FDA for treating acne. Unlike salicylic acid, it's almost always called out as an active.

Azelaic acid: Over-the-counter options of azelaic acid usually aren't regulated; however you can get it in prescription strengths to treat rosacea in which case it's, of course, considered a drug.

Retinol/Retin-A/Retinoic Acid: These vitamin-A derivatives help increase cell turnover, thereby helping acne and fine lines. And the strength of the derivative depends on its classification. For example, prescriptions obviously are considered a drug by the FDA, whereas some OTC brands are considered cosmeceuticals.

Pro-, pre-, and postbiotics: These are various ingredients that help your skin microbiome by either feeding your current bacteria (prebiotics), place strains of bacteria back on the skin (probiotics), or provide your skin with the beneficial byproducts of the bacteria themselves (postbiotics).

Hydrators, like hyaluronic acid and ceramides: These are generally only cosmetic ingredients.