Back when Mosaic first popularized the web (early 1994 according to my faulty memory), it had a Home button which would take you back to a particular page of your choosing (or your sysadmin's default choice), which many people sensibly called a home page. All graphical browsers that I know of have followed this tradition of providing a Home button. Typically, this page is a convenience for the user, and provides a wide variety of links pointing all over the web.
Since those early days, it has also been customary for people, organizations, projects, etc. to provide a general introductory web page with an easy-to-remember URL, which welcomes users and points to more focused pages pertinent to the topic, most of which reside on the same server. One sensible term I heard applied to such pages was welcome page.
These two types of pages are vastly different in form and purpose. For some strange reason, the internet community now calls a page of the latter type a “home page”. Unfortunately, it appears to be too late to do anything about it.