What is the difference between a continent and a country?

Apparently, at least one member of the Wiley family and a member of the Shiro family was confident that Europe or Africa are countries.  I post this here so that we do not repeat their same mistake.  As the old addage goes, those who do not know their history are doomed to repeat it. 

According to an online dictionary, a continent is "one of the main landmasses of the globe, usually reckoned as seven in number (Europe, Asia, Africa, North America, South America, Australia, and Antarctica)."

According to the same source, a country is "a state or nation: What European countries have you visited?"The idea is that there are many countries within a continent. 

This concept at least is pretty basic.  A more interesting question for a future blog may concern what exactly makes a country a country.  For example, why is Lesotho in Africa considered a country and Texas just a state within the United States?  Considering the sizes of some of these countries I wonder sometimes what exactly constitutes a country as opposed to a city like New York City or a state as in the state of New York? 

Is it merely a declaration of political independence from a higher governmental authority?  I wonder...