Machine Learning - Where is the difference between one-class, binary-class and multinominal-class classification? Where is the difference between one-class, binary-class and multinominal-class classification?

If I like to classify text in lets say four classes and also want the system to be able to tell me that none of these classes matches the unknown/untrained test-data. 

Couldn't I just use all the methods that I mentioned above to reach my goal?
e.g. I could describe C1, C2, C3 and C4 as four different trainings-sets for binary-classification and use the trained models to label an unknow data-set ...

Just by saying, Training-Set for C1 contains class 1 (all good samples for C1) and class 0 (mix of all C2, C3 and C4 as bad samples for C1).

Is unlabeled-data C1 -> 1 or 0

Is unlabeled-data C2 -> 1 or 0
... and so on ...

For multinominal classification I could just define a training-set containing all good sample data for C1, C2, C3 and C4 in one training-set and then use the one resulting model for classification ...

But where is the difference between this two methods? (except of that I have to use different algorithms)

And how would I define a training-set for the described problem of categorizing data in those four classes using one-class classfication (is that even possible)?

Excuse me if I'm completely wrong in my thinking. Would appreciate an answer that makes the methodology a little bit clearer to me =)
The difference between these methods is the assumptions they make about the task.  Multi-class classification assumes that each document has exactly one label.  So a document can either be about sports or weather, not both.
Multi-label classification allows a document to have any combination of labels, including none.  So a document can be about only sports, only weather, sports AND weather, or neither.

You could train a multi-label classifier with data where each document has exactly one label, but there is no guarantee that the predictions made at test time will have only one label.  Also you are forcing the classifier to do more work (and potentially make more errors) by considering more possible labelings than it needs to.
Therefore, if the multi-class assumption makes sense for your problem, you are better off with a multi-class classifier.

The method that you describe for training individual binary classifiers corresponds to multi-label classification.  The binary classifiers that you use could each be trained from one-class data or two-class data.  However, this is only one of the many ways to do multi-label classification (see the wikipedia page above for more).

Unfortunately, the problem that you describe does not cleanly fit into either multi-class or multi-label classification, since you want each document to have at most one label.