I would say Eurasia is the continent and Europe just part of it. When I was at school there were only 5 continents in the world. Depending on convention models there are either 4,5,6 or 7 continents.
For me Europe is a region area.
Wiki continents:
Since when Australia is a continent?
Australia is a country in a continent called "Oceania" where you have tons of islands, New Zealand, etc...go tell a Zealander that he lives in Australia...lol
Then you have America (divided in three parts: North America -Canada-USA-Mexico-, South America -from Argentina up to Panama´s canal- and since I was in college Centre America were all those little countries between Mexico and Panama) , Europe (from Spain to the border with Russia), Asia and Africa.
Antarctica is taken by a continent as well.
Europe is not a region and not a part of it...is a whole continent alone and Asia is other continent. Both united form Eurasia but is not taken as a whole continent.
I also read one thing right now and that´s why "we are confused", and that is that in some countries where people speak in English (USA, Canada, UK) and despite the language in China as well, at school they learn continents in a different way than in the rest of the world. (not sure why, maybe because you want to feel special, not a clue really...lol)
In resume:
So for North Americans and Chinese goes like this: North America, South America (not sure why you divide America in half), Europe, Asia (but you join it so ends up called Eurasia), Africa, Australia (which to me this is so wrong in some many ways) and Antarctica. (which for some is not considered a continent yet)
So for you there are 7 in total.
But I was born in Uruguay and now I live in Spain, and in both countries we learn this way: America (divided in 3 parts/regions, South, Centre and North), Europe, Asia, Africa, Oceania (Australia as a country which is in it) and Antarctica.
So for "us" there are 6 counting Antarctica.
Eurasia is called that way because both continents (Europe and Asia) are in the very same tectonic plate. So in conjunction you can call them a whole continent but tell that to an European or a guy from Asia...lol
Also as a reference, Turkey has a famous city called Istambul (the former Byzantium and then Constantinople)...which is known because is "divided" in 2 parts...one is in Europe and one in Asia.
Australia can be taken as a continent alone because of its size but it is not because is just a single country, and the rest of islands (for example New Zealand, New Guinea and such) are not a part of it of course.
Also one more huge reference...the Olympics. The symbol of the Olympics are 5 rings and each one of them represent 5 continents which are: America, Europe, Asia, Africa and Oceania. (Antarctica is not represented of course since there is no country to take part from there)
Let´s hope to see a guy from Australia say something about this because this is a mess...I can´t believe we (people from the very same world) learn different stuff just because we speak different or live in a different part of the world.
This is so wrong...
Edited and fixed some bits. I did a better research.