(sorry for the double post)
In Dutch there are two different words for what is called continent in English: continent, and "werelddeel", translated as "worldpart". The continents are Europe, Asia, North America, South America, Africa, Antarctica and **Australia**. The "worldparts" are Europe, Asia, North America, South America, Africa, Antarctica and **Oceania**. There are many other definitions of worldparts, sometimes Central America is considered separate from North America, and sometimes Antarctica isn't even mentioned. That's because worldparts are more cultural/politically based divisions, rather than geological. Other distinctions include Greenland and sometimes Israel as part of Europe (not French Guyana) and indeed, Hawaii as part of North America.
Also, worldparts include islands that are not on the actual Continental shelf (cyan in [this](http://upload.wikimedia.org/wikipedia/commons/9/93/Elevation.jpg
) image), such as Iceland.
Iceland geologically belongs to both North America and Europe, it literally on the edge of the two. Also, New Zealand is not part of the continent Australia, but it is of the worldpart Oceania, and so are Micronesia, Polynesia, Melanesia and partly Indonesia. And, Europe and Asia are often merged into Eurasia, and sometimes even Eurofrasia. (Europe+Africa+Asia)
So far the Dutch definitions. It looks like you are arguing about whether to use continents or worldparts, or a combination of both.