The word hypertext means same in both.
Hypertext is related to the content of a document. It could be text, image, sound, video in a document which is marked as a link to some other object or page in another or same document. When hypertext is clicked on we travel through document to new location. We can traverse through multiple documents progressively to higher levels of details. HTML documents - hypertext mark up language documents or web pages are hosted on servers and displayed through a web browser.
http is a hypertext tansfer protocol. It is a computer to computer information transfer protocol over a network. This protocol sends and receives hypertext based documents - for example HTML documents. A computer server listens to a client computer request to display a web page (HTML) at a universal resource location URL on the server. It sends the page to client and is displayed in the browser of the client PC.