The short answer is that there's no particular way anyone would have known that the settlements on Greenland and (briefly) Newfoundland were attached to any kind of a larger continent or nearby landmass; this isn't like Civilization where you get "your explorer has discovered a new continent, they're naming it America!" (We also get similar questions about trade and contact between Siberia and what's now Alaska; people knew there was more land over there, but it wasn't attached to a conception of North and South America.) Globes of the early modern period -- that is, of Columbus' time -- showed "Cippagnu," that is Japan, as being an island chain that was west of Europe, with nothing much in between (I wrote more about the maps Columbus used here if it's of interest). From that answer:

We know that he corresponded with Paolo dal Pozzo Toscanelli, a Florentine scholar who believed that sailing west would be a feasible way to reach Asia. Toscanelli had a map, possibly based on Martin Behaim's globe, that showed Asia extending much further east than it does, and the Azores, Canaries and Cape Verde islands extending much further west than they do (the Azores would end up right off the coast of Labrador in Behaim's projection).

The other factor to consider is that Norse settlements in Greenland were never particularly large, and the settlement in Newfoundland was only occupied for about 20 years (and there's debate over whether it was even a permanent settlement). The Norse made contact with some indigenous groups, but never on a large scale that would necessarily lead to further exploration.

As to why Columbus is better remembered, his "discovery" came right at the cusp of an entire age of exploration that Europeans enthusiastically participated in, and precipitated not only colonialism but the genocide of native populations in the Americas. Lots more in our faq about this, and also the Norse.