Från wikipedia:
A home page or index page has various related meanings to do with websites. It can be used to refer to:
When the user first opens a web browser, it automatically brings you to this page, which is also sometimes called the start page.[1]
It most often refers to the initial or main web page of a web site, sometimes called the "front page" (by analogy with newspapers).
The web page or local file that automatically loads when a web browser starts or when the browser's "home" button is pressed; this is also called a "home page". The user can specify the URL of the page to be loaded, or alternatively choose e.g. to re-load the most recent web page browsed.
A personal web page, for example at a web hosting service or a university web site, that typically is stored in the home directory of the user.
In the 1990s the term was also used to refer to a whole web site, particularly a personal web site (perhaps because simple web sites often consisted of just one web page).
Med andra ord, hemsida som synonym för site är föråldrat (och fel från början i vilket fall).