North America and South America are different continents...
The boundaries that make up continents are to a degree arbitrary and depend upon the person making the statement. There's no real justification for Europe being a continent; Europe and a large part of Asia are on one tectonic plate, while the easternmost part of Asia is on the same plate as North America. And the Indian subcontinent is on yet another plate.
So, it's ultimately local custom that determines the number of continents. I've seen Europeans refer to the Americas as one continent. For example, the Olympic rings were at one time intended to represent five continents.
The Olympic flag ... has a white background, with five interlaced rings in the centre: blue, yellow, black, green and red ... This design is symbolic ; it represents the five inhabited continents of the world, united by Olympism, while the six colors are those that appear on all the national flags of the world at the present time.
-- Pierre De Coubertin (1931)
(The quote's copied from Wikipedia, so in five minutes it's entirely possible that De Coubertin would have said the flag represents the population of elephants tripling within six months.)