What you're describing is "second intention" healing: the act of the body healing a wound without closure. It's unnecessary (and sometimes impossible) to suture every wound. Not much to glue together on, say, a skinned knee. Second intention healing actively scars over as fibrin (manufactured by your liver) knits a structure together for cellular regeneration. That's why a scar looks different from your usual skin: it's literally built over a scaffolding that your body isn't made of normally.

It's common and harmless, just letting a wound granulate in. Usually best for superficial wounds like abrasions, though I've seen it with deeper wounds on occasion. In both cases I can think of immediately, the wound was bandaged with honey, which acted as a secondary granular structure while also protecting the deep tissue from infection. Eventually the skin grew back in, though both times it did scar rather spectacularly. The doctors on each case felt sutures would be difficult and risky, based on the mobility of the sites as well as poor "margins," which are the edges of wounds. Without proper margins, they're nothing to really suture. Imagine taking a half-dollar sized patch of skin off your wrist: how do you put the edges back together on such a wide, mobile space? You don't. You let it heal by second intention.

Sutures (and staples) come in to play with lacerations mostly. Nice, deep, linear wounds with most of the skin still available to suture. But that's a different subject.

Your two biggest organs - your skin and your liver - are also the only two with active regenerative properties. That doesn't mean take them for granted, but do have a little trust!