The different between hosting wordpress ourselves and making one in wordpress

I just wanna to have a quick idea of what are the differences to have a wordpress in a total different domain, or to make on and host in wordpress.

I know some different as I have installed wordpress, like to have an unique domain name, but hard to install the wordpress stats as there’s API problem…..

My blog is one I host under a domain.
https://www.cheekykid.com/blog/