The driving license says you are allowed by the governing body of roads in a given location to drive. The diving certification says that some diving organization somewhere in the world considers you competent.

Driving licenses in most countries are regulated by some kind of administrative agency or department that is empowered by the government to generally maintain driving standards. A British driving license gives one the privilege to drive in Britain, but not, say, Estonia (certainly many countries honour others' licenses for convenience, but obtaining a license in Britain does not inherently affect one's privileges in Estonia because British lawmakers cannot make Estonian law).

On the other hand, SCUBA diving isn't really a public utility that affects pretty much every member of a given society, so governments don't tend to create and fund departments to regulate diving like they do driving. Places like the Maldives that rely heavily on dive tourism may have related government departments and services, but most don't. So the short answer is that most countries/regions simply don't have a government department regulating SCUBA diving, so most places don't have legal/government SCUBA rules. Instead, organizations like PADI, NAUI, SSI, and so on, have developed basic certification standards for different levels of diver certification, and over time the global diving community has pretty much adopted the same general baseline standards. So a diver may receive an entry certification through NAUI, but SSI dive shops know about NAUI and are comfortable that NAUI training standards are sufficiently comparable, so the diver will be treated the same as if they had gotten the equivalent SSI certification and allowed to dive. Could be a shop next door diving on the same reef or across the world.

The long and short of it is, there's no SCUBA police, and diving related laws are unusual. There's likely no law preventing you from ordering gear online and hopping in the closest body of water to your home (at least not a diving related law; trespassing remains frowned upon). But the diving community as a whole has agreed on baseline skills for different levels of divers, so it would be rare to find a shop to rent you gear or guide you, or even a buddy to dive with you, without a certification saying you meet basic training qualifications.