Copy/Pasting web content into $Text is akin to pasting RTF/rich text styled content into $Text. Weblinks and any any supported style features (text colour, font, weight, emphasis) is retained. If SmartLinks are enabled (the default) any weblinks in the source data should be detected and adopted as functional Tinderbox weblinks.
Using Paste-and-Match-Style (⌘+⌥+⇧+V) plain text is inserted. note that any links are lost as only the anchor text is retained. Actual URLs in text will be retained but will not be active links.
Pasting webpage content into a note also sets the receiving note's $URL to the URL of the source web-age unless the note already a $URL value. Thus if pasting from multiple sources, only the source URL of the first page is stored, or none if the note already has a $URL value for some other reason.
See also: dragging web content into view panes.