It sure isn’t! GitHub Enterprise Cloud is simply an enterprise plan on the regular multitenant github.com. Your repositories are on disk right next to everyone else that uses github.com. There is no segregated storage or compute.

I wish they had a plan to literally host GHES for you because then more people in the company would be forced to reckon with how terrible GHES is from an operational perspective. It is stuck ca. 15-20 years ago conceptually.

Github enterprise cloud is on github.com and with more features: http://github.com/account/enterprises/new

They don't host github enterprise server for you (though gitlab has something called gitlab dedicated which they host gitlab ee for you).