These are interesting questions, and more than just a matter of arbitrary choice. North and South America are geologically separate continental masses. The isthmus between them is relatively recent in date, whereas the hearts of both North and South America are extremely ancient and have been dancing separately (and occasionally fused together) about the surface of the Earth for most of its 4567 million years.
Europe and Asia are currently one continental mass, what I call a “megacontinent” composed of many separate ancient continental fragments, now fused together at sutures marked today by mountain ranges. You mention the Urals – this range anneals Europe to Asia. The Himalayas anneal India to Asia, and so forth.
However the other continental masses, each with a core of ancient rocks, are currently riding around separately – Antarctica and Australia, for example. This has been happening since the last “supercontinent” broke up, 270 million years ago. A supercontinent comprises all (or nearly all) of the world’s continental cores in one landmass.
This supercontinent (Pangaea) was the latest in a series of supercontinents that have formed roughly every 500-700 million years or so. Pangaea was composed of two megacontinents, the southern one comprising Antarctica, India, Australia, Africa and South America, and the Northern one comprising North America and Greenland, Europe, and much of Asia. (The Urals formed long before Pangaea came together).
The current drift phase will end in about another 250 million years with the formation of a new supercontinent. We think. But nobody will ever be able to prove it one way or the other, because the chances of our species’ surviving until then are probably nil.
You can read more about this is my book, 'Supercontinent, 10 billion years in the life of our planet'.