Buying domains are not for anyone. Only “authorized” entities can do that. Generally, they are host providers.
Google, GoDaddy, iPage and many more can do that. They buy the domain for you and they register that domain is yours. Then, they add that domain to the list of all domains that exist in the world. After doing that, periodically that list is sent and refreshed in all hosts in the world.
Then if you buy it in Google and host your site on google, imagine your name is “myweb.com” and you buy that to Google. Google tells the world When someone asks for “myweb.com” ask to me… I have in my host that domain. That info is replicated for all hosting providers.
By the way…. you can buy the domain to one provider and have your files on the servers of another provider. You can do that configuring it. That only changes that “map” and is replicated again to all the world. But you should renew your domain each year with the authority you register it. If you want to change that, you should “transfer” your domain to another provider (It’s only asking and authorizing that)